Some old man at the range once told me "Two types of rifle: shot alot & carried a little vs. carried alot & shot a little". A hunting rifle is usually light with acceptable accuracy and a target rifle is heavy with accuracy due to a heavy stiff barrel.
Since you did state .308, an excellent round for both target shooting and hunting, I would recommend a shorter barrel. The .308 does not give up much velocity by dropping to a twenty inch barrel. This is what I bought:
Centerfire Rifles - Tactical - Model 700 XCR Compact Tactical - Remington Rifles
"XCR" stands for Extreme Condtions Rifle and is weather resistant coated stainless steel, it has a short and stiff barrel, and Remington's 40x target trigger (nicest factory trigger I've ever shot). Most importantly, it weighs under nine pounds scoped and also is very handy with it's carbine length.
The .308 is adequate for most North American game and the round is 1000 yard target shooting capable even in that short little barrel (use FGGM 175gr rounds). I find it to be a perfect compromise for the question you asked, and mine shoots right around 1/2 MOA. The Remington 700P LTR (Light Tactical Rifle) from their Tactical is the same basic rifle in chrome-moly instead of stainless, and still has the 40X trigger (since late 2009) for a couple hundred dollars cheaper. There is much more web info on the LTR since it has been out longer, they are historically very accurate, usually 3/4 MOA or better-look 'em up.