Yugo Mauser!
If you must limit yourself to those three, I'd go with the .30'06. Between that and a .22 you can deal with anything in North America.
HOWEVER, in my experience, most old .30'06's (1903 Springfields, M1 Garands, etc) are increasingly expensive. Unless you're in the CMP, you'll probably pay thousands. New .30'06 hunting rifles start at $500 (plus a scope) and go up and up. I'd suggest getting an unissued Yugo Mauser instead. You can get a complete package for $150-$200. The 8mm Mauser is the cartridge which inspired the .30'06. It's plenty powerful if you stay away from domestic ammo.
I've been extremely pleased with my Mauser. It's tough, accurate, powerful and probably the best buy I've ever made. They really don't make 'em like this any more. It's the next best thing to getting an unissued Springfield, and a whole lot cheaper. I was so happy with it, I even changed my username to Cosmoline ;-)