If you are going to be shooting a LOT, you will probably want to get into loading your own rounds. I have been doing this for years with the .308. I can load 110 grain rounds for smaller game and 180 grains for larger game. All the other calibers mentioned are good choices, but since we only have a couple of places to buy ammunition here, I got tired of only being able to get a couple of different grain loads with factory ammo, so I started loading my own. Costs about a 3rd of factory, and shoots a lot better in my rifles.
If you are NOT going to be doing anything but hunting with the rifle, then you probably don't want to go into the expense of loading equipment, although it only takes a few boxes of loads to re-coop your investment.