Your buddy picked an excellent calliber to begin with. There are oodles of bolt action .308's out there for well under his budget. Check out GunBroker.com He should be able find one no problem. The older Remington 700 BDL's, Model 70's and Ruger 77's are no longer "in style", so should fairly priced. I've owned and shot a Model 70 and a Ruger 77 in .308, and currently own a Mauser in said caliber. All were/are just crazy accurate; all grouping easily well under 1" @ 100 yds. with good handloads.
A co-worker bought a Tikka (sorry, don't know the model) at the local Academy and put a Leupold 3-9x40 on it all for around $800. He shot it here at the house on my range with Hornady factory ammo as well as some of my handloads and it was INSANELY accurate easily grouping 3-shots @ 100 into 1/2" over and over. Excellent shooting from a sporterweight hunting rifle.
Another long forgotten rifle is the homely, yet super accurate Remington 788. A close friend has one in .308 and I've handloaded for it for 20+ years. It too easily groups under 1" at 100 yds. with an occassional group around 1/2".
The 308 is just one of those cartridges that for whatever reason shoots well in almost any rifle.
Regarding the scope, I'd discourage him from a fixed 10X scope. It would be fine at long range, but in hunting situations, it's inevitable that a nice buck will show himself at 20 yds. where a 10X scope is as useless as the proverbial teats on a boar hog. A Leupold, or better yet Burris, 3-9X32 or 40mm will do everything he needs.
Good luck,
35W