Alrighty, Nichole requested me to do this for everyone (or just for her lolol). So here's a list of my personal opinion which ones are the best for people to start with, notice it's my personal opinion so by no means the best choices for everyone. Some people may find other champions better for beginners!
Stands for Attack damage carry. ADC is most of the time an range AD based champion that lanes at bottom with a support. Their job is to deal damage to whoever is closest and stay at a safe place. Yes, stay at a safe place and attack the closest target, even if it's a 300 armor Malphite. That is your job as AD. A lot of people might yell at you that you are focusing their tank instead of focusing their carry. Of course, you can focus their carry if it's safe to go for them, but if there's their tanks blocking the road and they are staying behind, it's not worth going for them. Because by the time you get there and shoot them few times, you'll most likely be dead already.
Just a general info to give you the mindset how you should be playing the AD, not going too deep with this as this thread's point isn't that anyways. lol
In my opinion one of the best AD carries to start with. Firstly, she is free (Liking Riot on Facebook) so if you would like to try how does beng ADC feels like it's a really good choice.
The fact I put her at top 1 is because of that her kit is really beginner friendly. You get a jump which can be used for escape from bad situations which might happen often because of the bad positioning as beginners can't do it that well yet. Also on top of that her passive gives you extra attack range, and when you are lvl 18 your attack range boost will be really helpful for positioning even if you aren't good at the beginning with doing that.
Last hitting in tower might be slightly harder for her due the explosion shot dealing damage AoE to the mobs so you won't be able to easily last hit "normally", which means melee minions would be 2 turret hits then you can last hit and range minions 1 turret hit and your last hit, but you'll get used to it real quick.
She's really cheap, few games and you'll have enough IP for her. She won't be one of the easiest AD to play, but she is really cheap and good for learning how to play AD the fact that positioning with Ashe is really important because she doesn't have any kind of speed buff, gap closer and a small attack range. Only thing she has is frost shot/volley which slows and ulti that stuns, so with this at the same time you'll learn how to kite as an AD. Just make sure you take an advantage of your frost shot on kiting. Hit the enemy, then back off abit and then hit them again. Don't stand still. It might be hard at the beginning, but once you get used to it, you'll perform a lot better with teamfights.
Honestly, I would rather skip the third AD spot because a cheap and easy to play ADC doesn't really exist apart from the 2 listed above lol. But easiest to play with low price would be Sivir I suppose. She won't be the easiest one to play in team fights, that's for sure, because of her low range and no CC/escape at all, so if they have any hard engages or assassins you'll be quite in a trouble, let's say if you are off position and they have a Fizz that notices you off position, you are in quite a trouble lol.
Apart from that, her laning is quite easy due the easy wave clean with the boomerang and ricochet. Unless if your enemy is something that has good poke or long range, that way they could easily deny you from the minions, Sivir being small range and stuff lol. She is best to be played offensively, in my opinion. Something like Alistar/Taric as support makes the lane really dangerous for the enemies because if both you and Taric get all the skills off, their AD/support is quite much dead.
(Notice : Both Ashe and Sivir are really easy to get, and fairly easy to learn how to play them, but to perform well with them, that's something harder.)
AP standing for ability power. Most of the time they are being played at mid. In mmorpg terms, they are pretty much the mage/casters. They can be also be played at top, for example Vladimir, Elise, Akali etc. can be seen at top now and then.
Definitely best mid champion to start with for beginners in my opinion. Really easy to play, really cheap, and not that punishing with mistakes in positioning due the item build you get for him makes him tankier than other mid champions.
Notice though, Ryze's mechanics are different from the other AP mid champions, because the fact that his skills benefits from both of your max mana amount and your AP. But in general this top list is for mid champions and he is mostly being played at mid so it's still a correct place to put him in.
As stated earlier, he is easy to play. Shortly said, you just pretty much in fight cast all your skills lol. There's small combo/trick for him for ideal damage dealt though. Which is : Q/E and before the ball or the disc lands you activate your R so that you would both gain your ultimate extra dmg on that skill also reduce your skill duration by 1 second. You shouldn't always aim to do this though. For example if you are trying to catch up to someone with your team then activating your ulti to rune prison is a better choice.
She might not be the easiest mid champion to play due the bind is skill shot. But she's cheap and fairly easy to farm with, that's why I put her at the second. i also put her this high for the reason that she's a good opportunity for players to learn different stuff about the game, and Morgana is good for that soft landing to learn more how the game works with skillshots.
She's really easy to last hit with, especially the later of the match, when you have enough AP just put the puddle and the minions dies.
In teamfights she's quite easy too. Just throw the bind and a puddle under those you wish to target, and if a chance comes when you can ulti on few of the enemy team just do it.
Annie being lower than others on my list mostly just because of the fact that she is said to be easy to play but in my opinion it's quite hard to perform well on her, especially in fights. The thing is that she has lower range on skills than most of the other AP.
So why am I still putting her on the list though? Well she is cheap, just like all of those other champions I've listed, also because she's quite easy to farm with. With the W and enough ap you can just clear the entire wave. Also early game you can spam the Q to last hit as it gives you mana back. I somehow learned how to last hi tbetter in general just because of that, I don't know if it works for other people though.
Also if you did well during the early game, with a stun and then throwing all rest of the skills on the enemy, you would deal a nice burst damage to the target. That is also why I put Annie on the list after all, because it doesn't really require much to deal high damage on Annie, so it's fairly newbie friendly regardless of being harder to master her.
Jungler's role is to farm in the jungle (Well duh). They also handle most of the ganking during the laning phase if there's a chance for that.
Most of the time jungler nowadays are quite tanky and sometimes a front liner, but they also can be more offensive ones such as Zed or Kha'zix for example.
wiki site for jungling which covers the basic infos about jungling, because I don't really play jungle unless if I am forced to without any other roles open, I don't really know much about them and the top list can be slightly incorrect because I haven't jungled without runes ever since I bought my first runes, so I don't really know how well the champions works without runes so apologizes for that.
For sure the best jungler to start with without runes, because of the amount of sustain he has in the jungle, he won't have any problems even without the boost the runes would give him.
Easy to play, most of the time in the jungle you pretty much just auto attack, with a blue buff you can pretty much spam your attack speed buff and Q to lifesteal the minion without having any mana problems.
He is hard to gank with pre-6 because he has pretty much nothing, no gap closer or any CC before you get your ulti, but Warwick is still a really good champion to pick up to learn the basic stuff about junglers. When you get 6 it gets quite simple how to gank, you just gotta ulti the enemy and they are gonna stay still for your team mate to attack freely for few seconds lol.
Another champion that allows you to jungle without runes because of the life drain.
Just like Warwick, when he gets 6 his ganking becomes much stronger, but the difference is that Fiddle can also make really strong ganks with the correct ganking path choice because of the fear.
Also I do think that Fiddle is a good champion to learn more about ganking, as you will be trying different routes out for the ideal ganking angle where the enemy's gonna have hard time to escape from.
Slightly more expensive than other ones, but I really suggest trying him out though if you see him on rotation and is interested in jungling.
Personally I find that it's really easy to jungle with him with decent fast clear time.
Just like the 2 earleir champions, when Nocturne reaches 6 his ganking will be a lot easier, and really strong at the same time, but just like fiddlesticks, nocturne isn't ulti dependant. With the movement speed buff from the Q and the fear, he can easily do some nice ganks even before reaching 6-
Well so far all the champions I've listed are really cheap to get with IP, so throwing in Nocturne was kinda unfair, so here's second choice fo rme on the third spot
Anyhow, I haven't really ever jungled with Nunu more than once or twice so i don't know how well is his sustain without runes, but i guess he will be able to pull it off. He is someone who can gank whenever he wants, because of the bloodboil and iceball, he can make some good ganks fairly easily if you just come out from the right place.
Apart from that, not much to say about him lol.
In general : All of those champions ganking ability changes a lot when they reach 6, but notice though, you can always gank even without ulti. Especially with Fiddle and Nocturne. Well why not warwick too, but it's gonna be harder, unless you come from behind with red and the enemy doesn't have any escape/summoners. Such as Mordekaiser is easy to gank if he doesn't have summoners.
Well shortly said, those who plays at top. lol
Because nowadays there's so many kind of different picks for top, such as ap, or offensive top etc. But mostly let's say top most of the time is quite tanky, if not a full tank, but as I said, it keeps changing nowadays so won't guarantee your top will be a tank though lol.
But I will be listing the tanky ones.
Hands down one of the most common picks for the lower level summoners. There's like, garens everywhere lol. For a reason though, he is really cheap IP wise, and extremely easy to play and naturally tanky because of his W, while activating it makes you even tankier for awhile. Eventhough he does scale off quite quickly when late game comes, but it's still a good pick for those who would like to get a taste of how does it feels like being that meatshield running in and spinning.
Not easiest one to play because you might miss a lot of your taunts at the beginning of trying him and you won't be able to use the ulti that well, but he is cheap to get and really tanky. If played correctly, it's hard to force you off the lane too.
He might sometimes be banned in ranked games, but since this is for beginners those champions, that won't be a problem lol.
A rarer pick nowadays to be seen at top, but it's still totally viable. Not that hard to play after learning how to play him, which after that the laning becomes easy, because of his passive, you can farm a long time in lane befroe you are forced to go back.
Along with his ulti stacks you will be really tanky late game, make sure you get some tanky items though, full AP Cho gets teared down real fast lol
Those who lanes together with the ADC supporting them so they can farm. They don't really take any creeps unless if it's a must. For example that AD won't be able to get those minions, let it be that they are back, or that they won't have enough time to get it because there's more than one minion who is about to die.
Well she's good one to start with. Gives you general idea what a support should be doing, along with that you will actually will be able to "support" your laning mate by healing and giving them mana back. That doesn't mean you are just simply a healer who runs if a fight happens, you can also play slightly more offensive if needed, such as starcall them or silence. Just make sure you aren't spamming the starcall though, because you shouldn't really be doing much damage in the end with it so it's not really a viable poking way, also your laning mate would prolly start raging at you lol.
Just like Soraka, she is someone who sits around and protects the carry. The difference is that Sona isn't as defensive as Soraka is, she can poke and also be offensive on lane if you want to. Once you get your ulti you can engage on them as stated earlier, you can be offensive or you can save it and wait for the right moment, such as that you must fight and no way to run and use it for defensive and try to change the fight that way.
I put Taric lower than the other two, because he is most offensive one out of the three. Eventhough of course he can be played as really defensive if wanted, because of the fact that he can heal and gives bonus armor to the laning mate just simply by being around. You can get most out of him by being aggressive though, that's really your choice.
Alrighty that's it, just a short list and explanation why did I choose them. Also remember, you don't really have to play those champions at the beginning if you are new. In fact playing some hard champions might even be more profitable, the fact that you will be able to improve in the game faster that way. Such as learning how to hit with skill shot. etc.
Also yeah some of those pictures are of the old champion icons. I just grabbed those real quick from the all pictures thread lol
Edit: fixed the new images