Guys I need help. I stink at the game and I want a champion that can fit my gameplay style. Please and thank you. If you don't agree with any of the champions below don't be afraid to comment one that would also be good too :)
Depends on what role you like to play. I like the ranged/ADC role, and I think Sivir is tons of fun. Jinx is also, but she's sooooo squishy.
Of the two you mentioned, 
Teemo is the simplest. He's ranged, quick, no skillshots, and Ali just has some nuances to him that make him difficult (you can really screw up with headbutt easily).
Other random recommendations: 
Ashe is by far the most straight forward ADC to learn on, though if you're confidant enough (and have the IP for it) give 
Ezreal or 
Caitlyn a try, who are also relatively straight forward but have the advantage of having a dash/blink to make up for mistakes.
Garen is a good tank to learn on, simple and cheap; his big disadvantage is he doesn't have a gapcloser, but he at least has a speed up.
Soraka is an easy champ to learn support on. I also have to recommend 
Sona, who is even easier, just a bit more expensive. The biggest problem is, higher level, these guys aren't super popular right now. No harm in using them to learn though. Healing is always useful.
If you have any more questions, feel free to ask. :)
What role do you usually play? I can make recommendations based on it.
Best advice I can give is save as much ip as you can until later levels (like 25-30) and BUY RUNES. As far as gameplay, try and get used to playing quick cast (in your options menu, I would suggest reading about it. Last hitting is going to be insanely important. If you want to get used to quick casting and last hitting fast, play a mid champ. It will force you to solo, learn to wave clear, and quick cast abilities. A good champ for wave clearing and learning skill shots (quickcast) is ziggs.
With Ziggs, make sure that, at first, you are playing somewhat passively and timing/aiming your shots (while anticipating movements) so that you can get used to the animations and mechanics.
That's just my suggestion if you want to learn quick. As far as the two champs that you have, Alistar is underrated. He is essentially a tank for bottom, which may also be a good beginner champ and learning bot mechanics, while staying alive. Just make sure you act like a tank for your adc, and land those knockups at key moments.
I wish you the best, and feel free to add me anytime. I'm still fairly new to the game myself, so I know what it's like.
Hes really fun and op.
You never actually said what your play style is, but never fear. To start I would suggest different champions than what you would see at a higher competitive level.
If you want to just straight up want to faceroll with auto attacks, then I would suggest:
to start and then move into either or 
as they are all very straight forward. Caitlyn just fires from a range that is further than I believe anyone else naturally has, and Sivir allows you to use some skill to stop an enemy skill from hitting you.
Support I would say and are the easiest to learn at a base level. Just heal the person doing the damage and harass an enemy hero when you get the chance. Both have ults that can be absolutely game breaking in a team fight when used right as well.
Mid lane I prefer a little finesse to straight up facemelting. So I would say to start with 
or 
and then move on to 
or 
as your skills evolve.
Top lane is basically devoid of much in the way of options. Everyone is right by saying is the top laner of choice, though if you can get 
or 
you can learn diggerent approaches to how to play top lane.
Jungling really doesn't start until you have a better understanding of the game as a whole so I would be failing you by even suggesting a jungler for you as your game simply is not there yet. Learn the lanes first and how they work, then learn how different champions interact with each other and go from there.
Top Lane - Garen (Tank)
Jungle - Warwick/Garen (Garen's not the best but he'll teach you how to approach without fancy tricks or gap closers)
Mid - Ryze
ADC - Ashe
Support - Soraka.
All 450s, all basic champions to help you understand the wonderful world of their roles.
Garen is best for newbies. very op when you stack all defense on him. just read all the abilities and get to learn when to use your abilities it also goes with learning every champ( even if your new ) watch youtube also it helped me a lot
Alistar definitely has nuances, but his ult is very forgiving to bad positioning, and he can teach you how to manage mana/cooldowns. I'm a bit biased though since I basically only played Alistar until level 20. If you like being an unkillable CC machine, pick Alistar for sure.
i was about to say 
but you guys at riot just defiled his corpse by feeding it to a grinder, nerfing him MORE? comeon, your doing the thing you did to 
and 
I would say you try learning 
or 
They are both simple champions that you can pick up for top lane.
I haven't seen him too much now and days
and well if you want to be the devil go for it
Totally depends on you, as and (I don't like either of them! Prefer 
,
, and ) seem to be the go starting ADCs and a lot of and starting out mid. Oh of course in the top lane you got Mr. Spin-to-Win , but really it's all on you.
My personal experience: When I first tried the game at level 1 or 3(after my friends begged me to try the game), I tried 
in which pissed me off to no end (she has a high skill cap, but she seemed so cool right?), so I try 
, better but it was still not my style, but at least I didn't feel like I was just dying and screwing up all the time, I still just hate the game... quit again, my friends totally beg me to try again, and then I see when I was looking at the free champions, pretty much fell in love with her, and I still love , I was able to grasp the basic aspects of this game with her, then tried again and I REALLY enjoy her, then I found 
I was more intrigued by her appearance of course, but I really enjoy playing her, and love how multi-faceted she is, you can play her top bruiser, mid AP assassin, jungle pretty much AP assassin, bruiser, or tank, you can even build her AD and hybrid.
As for supports, ya I started out with , then got into 
, then my now favorite 
, of those 3, is quite tricky with his hook having a wind-up animation time.
For jungle, (probably not seen at that level), or duo top 
, a decent with the right build will just 100-0 anybody.
Basically just take a look at the champions, find one you think looks interesting, then try them out, what someone likes may not be something you like, and what you like, may be something they don't like
and or
Support + Mid practice
ADC
Support Practice
Support/Jungle/Tank Practice
Top lane practice / tank practice
Mid / Sup practice, and ARAM kings.
Top AD / Jungle practice
Mid AP Practice
Defensive Sup Practice
Jungle Tank practice
I begun with Morgana. She might not be simple to play, however, there are some advanteges for a new player:
You can root enemies chasing you. When you do a mistake, you often end up being chased by enemies.
Many builds are suitable for you - really, you can build whatever you want and it will be good.
But honestly, I think the real skill is the cooperation with the team, foresight of the event progress and being careful. And with this it does not matter what character you play.
Alistair and Teeto are harder to play than they appear.
The first champion I mained was 
in which while her early game doesn't do much, but with her timing and appearance she can be quite devastating in team fights and especially in her lane with her shunpo being her main offensive and defensive method of attacking. You could either jump in randomly while laning and press on the attack or pop a ward down next to your tower (or wherever you prefer) and when your suddenly ganked can hop to safety. I enjoy her due to the fact she was quite mobile especially for ganks when you equip the right boots and such.
Teemo is better for low level than alistar.
