For a shotgun, I'd search out a nice Remington Express 870 for under 300 bucks. They're out there and you can adjust it to do whatever you want to do with a shotgun. Skip the other pumps and stick to an 870...you'll be glad you did.
A cheap rifle? How about one of the Yugoslavian Mausers or the German 98k Russian Capture guns that are on he surplus market? High quality guns that are accurate and reliable. An SKS is also a good idea if you are not shooting great distances and well within your price range. Ditto for a nice used Marlin 336 in 30-30.
good suggestions by brickboy per usual. I have a norinco sks i love dearly, i got it back in 1994 when i was a lil kid with paper route money, i am not a fan of the yugo SKS out there right now, cause they dont have chrome lined barrels. I would cruise some pawn shops or gun shows and get a SKS with a chrome barrel, its a great value gun.
I dont have a mauser yet, but i am gonna buy one as soon as i get my AR and FAL, i am in no hurry on the mauser since they wont get banned, but you can pick up some SWEET long barrel persian mausers made in czech for $200 , 8mm. I lust for one. Cant wait to get my other guns so i can get it.
Marlin 30-30 are pretty much the standard michigan brush gun for deer season. Half my hunting friends hunt with 30-30, cor bon has a sweet new bullet that really extends the range of the 3030 and the accuracy. Plus i always liked lever guns and bolt actions best, they are jsut more fun.
they yugo mausers you can get very good condition for $130 8mm.