I seem to do ok with the ranged champs ( Caitlyn, MF) but I feel that I am not helping the team all that much.
Stand behind your team and apply tons of damage to the closest target, you should be fine if you've farmed up.
-Some champions I found easiest to pick up-
AD Ranged: Ashe, Graves
AP Ranged: Morganna, Annie
Support: Soraka, Taric
Tanky DPS/ initiator: Warwick, Shen
If it's one champion that can fill a lot of roles, it's Gangplank.
This is just in my opinion, however. Also, remember to always try the free week champions, you might find one you really like.