308 is a fine deer cartridge and other larger game except maybe the largest bears.
I would search the used rifle market many 308's out there in some very fine rifles, Winchester model 70's Remington 700's and Ruger 77's, CZ 550, Howa 1500 to name a few. many have a decent scope mounted so the price is about the same as the cheap new models on the market today.
Al