If you're willing to spend the $60 or so,
The Ultimate Sniper by Maj. John Plaster is one of the most thoroughly written books on the subject that I've ever seen. It covers everything from rifle design, optics, ammunition choice, shooting mechanics, and stalking.
Do a lot of reading about desirable features, decide your budget, and choose a rifle that meets your specs within your budget. Be aware that you can buy a less expensive rifle and spend the extra money in your budget to have it customized to your spec (Rem 700s are, by far, the easiest to go with this route).
Orkan will tell you to avoid Savage at all costs. He knows a lot more than me, so I can't dispute.
I have a Howa 1500 that provided the base for my build. It came with a lot of specs that I would have had to pay a few hundred on a Rem 700 to do, and the action seems very stout. My plan is to shoot the piss out of it and keep it as my "training".308. Eventually I'll step up into a more custom rifle in a nice long range cartridge.
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