You should be able to find a new Savage, Rem ADL or Howa/Weatherby Vangaurd in your price range. The other option would be looking for a used in gun/pawn shops, want adds, etc. Not sure if your looking for something more than a 243, but I'd consider looking into a 7mm-08 which will offer more bullet choice, umf and similar recoil. Other choice's would be a 270win or 308 win both are excellent deer cartridges, offer load of offerings (guns and ammo) and managable recoil. 25-06 would be another one to consider but chamberings and ammo would be less then others mentioned.

Good Luck