.308 caliber rifle that fits this criteria.

[OrangePwrx9]

Reminton 788 .308 carbine. Hard to find but generally inexpensive (used to be, anyhow) and VERY accurate. They date back 40 years or more.

You seem them at gun shows. Other than that, gunbroker is your friend.

 

[sappyg]

The Remington model 7 sounds like it fits.

Saw a lot of Remington 600's at a local gun show last Saturday. Most were 243 or 6mm but they were below $600. 308's are around.