The 10/22 actually does feed just about everything short of CB caps and some subsonic ammo, but many of them are notorious for the extractor slipping off of the shell before it's extracted. Many of the stock 10/22 parts are made to... nonexacting tolerances, to say the least. I reccommend checking out
www.rimfirecentral.com to learn a bit about your 10/22, and you can also find some good online shops for aftermarket parts there,
HawkTech Arms, for example.
Since you're having problems with extraction, I would reccomend getting a Volquartsen exact edge extractor, which should eliminate most feeding problems. Also reccomended would be a Volquartsen target hammer, which will cut the horrible trigger pull nearly in half. If you decide to get the hammer kit, install only the hammer and not the springs that come with it to avoid light primer strikes.
Also check out Winchester Dynapoint ammo, which is available in bulk (500 rd boxes) for about $10 at most Wal-Marts or $13 at K-marts. I've had incredible results with this ammo... it's insanely consistent, especially for being bulk, cheap ammo.