For deer/yotes, I agree with .243. Based off the .308 but ballistically superior and can handle the game you speak of perfectly.

If you want a larger caliber in case of larger game, both the .30-06 and 7mm-08 are better options than the .308. There is nothing wrong with the .308 but honestly I think its popularity has more to do with its military legacy than anything else. It has nothing on the .30-06. It's hugely popular in tactical matches (legacy to military marksmanship), but in true target circles, at all ranges, there are superior options.