"...buy a whole bunch of different ammunition..." Sort of. Gets expensive though. If you don't reload, you have to try as many brands and bullet weights as you can in your chosen calibre. Same as you have to with a .22LR. However, you can narrow it down by calibre. The .30-06 and .308 tend to shoot 165 grain hunting bullets best. So you can try factory ammo with that bullet weight first. A 165 grain hunting bullet in either will take any game with no fuss.
Reloading is your best bet though. No factory ammo, as good as it is these days, will shoot as well as ammo that's tailored to your rifle.