All depends on how you are hunting. If you are sitting over a feeder, your deer rifle will work just fine. If you are baying with dogs... you need to be mobile.. and really a handgun (or a lance) are fine choices. If you are spot/stalking... I like a bow myself... but a shotgun is a great choice too.

Biggest one I ever killed was with a .22 Hornet... largely because its what was available at the time I needed it!