My recomendation is find a used 6.5x55. I was just married not to long ago, mortgague, school debt, etc.... I picked up my sportered swede for $100 with a 2-7 scope, it bagged me a 12pt buck last year! (My first year hunting). Still on a budget, I have managed to acquire a 6.5x55, 303 enfield, .222 savage, 12ga winchester, .22 cooey. None of these were over $200. 6.5 - $100, 303 - $100, .222 - $200,.22 - $30, 12ga - I traded for my SKS............ So there you go, fill a safe on a budget.
There are deals out there, just look for them and jump when they present themselves!!!
P.S. My vote is 6.5x55, mild recoil, accurate, and kills deer dead as it gets!!!! GOOD LUCK!!