RE: New .308
Since you asked about a bullet, I am assuming you reload. IMO the best weight bullet for a short action 30 caliber is a 165 grain bullet. You can buy the expensive bullets if you want, but in my opinion they are not worth the money they cost. The Sierra Game King bullet is a great choice. I also like the Nosler Ballistic tip bullets, they shoot great in my 30-06.
If you do not relaod-no problem. I would not waste my money on premium ammo unless you could not get the regular ammunition to shoot(accurately). Remington Core-Loc ammo is more than enough for deer hunting. Winchester Silver Tip's are just as good. Instead of buying expensive premium ammo-buy more less expensive ammo and practice.
Great rifle choice, and great cartridge choice. Try to find someLake City surplus ammo. That ammo shoots great, and should be cheaper to buy for practice. Tom.