So you want to play League of Legends - Part 2 - Pick a Main

So after a couple dozen games experimenting with free champions, you should probably consider a champion to 'main' for a while.
Having a primary champion will:
- Let you have someone to fall back to if you ever feel like you need to win a game
- Learn a champion indepth and hold a proper understanding
- Understand general matchups as well as specific ones (eg. How to play a Melee VS Ranged lane)
- Help you not suck
- Allow you to focus on what is happening in the game, rather than focusing on what your own spells are doing (this is an important one, as it will speed up learning of game mechanics as well as what other champions can do)

"But Meng! There are so many fucking champion in this stupid game! how do I pick just one?"
Well you've been playing the game right? You have 20-50 games under your belt right? Anyone stand out as looking awesome?
At some point you'll want to go through the champion list (Profile -> Champions) and just look at every single champion, look at all of their 4 skills. There will be at least a few that should stand out to you as sounding awesome. I Remember for me personally, I had my heart set on Pantheon.
Every champion is viable at low levels if you play them well, its only at the higher levels (or ranked) where certain champion picks become completely outclassed because of imbalance.

Eventually, you will want to have a main character in each of the roles (a bruiser for top, a mage for mid and a ranged AD Carry and Support for bot), so that you can balance out a team if you need to.

Other than your own personal favourite pick (whom you should be playing because you enjoy their playstyle) its nice to have alternate picks who are just generally overpowered - this helps in part by giving you a slight advantage over your lane opponent, and in making sure you aren't learning a champion - only to find out that they are useless at level 30 when your opponents are not going to be complete retards.

Here are a few general good picks for each role, with the ability to change the game when played well
The following go from Easiest->Hardest (eg. Easy, Medium, Hard, Harder)
Mages (Top): Vlad, Kennen, Rumble
Mages (Mid): Ryze, Kassadin, Lux, Ahri
ADC's (Bot):  Miss fortune, Graves, Ezreal
Supports (Bot) : Sona, Nunu, Lulu
Tanks (Top or Jungle): Chogath, Amumu, Nautilus
Bruisers (Top or Jungle): Warwick, Malphite, Irelia, Riven, Olaf
Assassins(Mid or Top): Talon, Akali

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Arrived from google? See also Part 1 - 'Basics/winning/roles/items'