The recommendations for the Remchesterby's are all well taken. If you would like to try something a little different, and of certainly equal and most likely better quality, get a CZ550. They have at least 3 different flavors, one of which will certainly suit you. Additionally, the 308's have detachable box magazines, so if you want to splurge you can get a high quality 10 rounder from them for not a whole lot of money.
I absolutely love my CZ. It is my favorite rifle to shoot any distances with, and 308 is my favorite cartridge for blasting with. I do find with today's prices, however, that handloading is a definite must.
Good luck and have fun with your new rifle.