The rifle's weight and stock design have as least as much to do with how you feel recoil as the actual caliber. A 30-30 has light recoil on paper, but the crooked stock designs along with no recoil pads on most of those guns amplify recoil and make it seem worse than it should be.
My first choice would normally be 7-08, but if a 308 bothered you that much, you may be better off with a 243. It should be fine for any deer hunting, but a little lighter than I'd like for anything bigger.
Stay with a bolt rifle to get the most rifle for the money. Lots of GREAT budget rifles to choose from right now. I'm really wanting to see one of the new Ruger American rifles that were just announced this week and are not in stores yet. Based on the features and projected street prices I think they may have a winner.
The Stevens 200, Marlin XS-7, Weatherby Vanguard, and several others are out there priced between $300-$350.