Browning makes a lever action in 308 (the BLR). My stepfather has two BLRs, one in 308, and one in 243. I used the 308 a couple of years ago deer hunting when I was having a problem with the rifle that I had brought. It is a sweet little rifle, and will put a deer down. Only downside that I can see is that if you are shooting from the ground, you may have to turn the rifle slightly sideways to eject a cartridge.

Semi-autos, whether AR or not, are a good choice, IMHO. I have a 30-06 Rem 742 and it has served me reliably for years. I believe that the semis are getting more accurate, at least from what I have heard, the ARs are getting more accurate. Sometimes you need a follow up shot quickly.

With that said, I believe that you can't go wrong with a bolt action. They are accurate, and why would you need more than one shot? Actually, I took two deer with my bolt action Sako last year, and one required a quick follow up shot. If you are experienced, you can move that bolt pretty quickly.