i've been hunting rabbits for YEARS and i suggest shotgun with field shot, or even dove shot.
small game moves quick, and since it seems that you're new to small game hunting you need to be super quick at times and your best bet then is a shotgun. you can find a used single shot 12ga for 75 bucks. my first shotgun was just that a savage single shot 12ga and it works like a charm for fast movers. i've killed squirrels, hundreds of birds/rabbits, you name it. definately one of the best buys.
but then again if you're lookin for more of a challenge i use my savage bolt action .22lr with a scope.