Versatility

[Mr. Zhu]

Haven't read through all of this yet, I'm just going to suggest 3 champs for each role that I think are pretty good to have in your line up over all.

Solo Top
Singed
Yorick
Nasus

AP Mid
Annie
Brand
Karthus

Jungle
Skarner
Rammus
Gangplank

Ranged AD
Vayne
Caitlyn
Tristana

Support
Sona
Soraka
Alistar

These are all really good picks for their respective roles, almost able to fit into any team comp.

Honestly though, don't worry about getting a specific champion for a role, there can be some flexibility in that, but do work on making sure you are competent with more than just 1 or 2 champions per role.

Would like to add to each role a little bit.

Solo Top
Renekton
Galio
Gangplank
Cho'Gath

AP Mid
Cassiopeia
Kassadin
Kennen

Jungle
Trundle
Nocturne
Udyr
Fiddlesticks

Ranged AD Carry
Ashe (Definitely pick her up as one of the first AD carries if you're looking to learn the role)
Graves
Miss Fortune (Feel like she's a sleeper)
Kog'Maw

Support
Taric
Janna(Low sustain but works with ANY ad carry)