You can't go wrong with a Stevens 200(under $300.00)in a 30-06, 270 win. 7mm-08 ,308 win.
These calibers you can cleanly take any game in North America, EXCEPT the Great Bears..but many have been taken with the 30-06 but it wouldn't be my choice ,I would hate to be Bear Crap !

Buckeye!

But you may want a Lever gun then you have the 30-30, 35 Rem. 444 M and the 45-70 and 450 M... My favorite is a Marlin 375 which is is a 375 Win. Caliber... The 444 M ,375 Win. 45-70 and 450 Marlin can take care of any game North America