Bruiser/top, Jungle, and Support.
You shouldn't just make a list and stay set. You're really new even at this point... I've been playing for 2 years, about 500+ matches, and I'm new too! Ashe is a good choice, if you own her. Here are my "best of" picks for the positions (a lot of these have some pretty steep learning curves, and require some practice... if you get to ranked, then most will be extremely useful... you'll be happy you learned them):
ADc: Corki, Ezreal, Draven, Graves, Nidalee? and Vayne. I would advise against Twitch... you might buy him later. Caitlyn's range can counter some ADcs... and Kog has incredible DPS, but requires some babying and skill.
APc: Orianna, Katarina, Elise, Morgana, Diana, Zyra, Annie, Ryze, Anivia, Ahri, Gragas and Akali.
Bruiser/Top: Darius, Shen, Malphite (possibly), Jax, Singed, Gragas, Yorick (a good Cho can counter), Cho 'Gath, Garen, Jayce, Nidalee?, Rumble and Lee Sin.
Support: Blitzcrank, Alistar, possibly Shen, possibly Nidalee, Nunu, Lulu, and Janna.
And Finally, Jungle: Amumu, Shen, Darius, Malphite, Maokai, Shyvana...
My opinion . Hope it helped.
(P.S.: I kinda used this to help http://www.reignofgaming.net/tier-lists/solo-tier-list )...