You have just described the Savage FTR in 308 with 30" barrel if you do not reload. you can get it for around $950 on Savage Shooters
308 is great to 600 yards, quality reloads from Black Hills is available if you do not reload. Barrel with last 4000 rds plus.
Here is the real benefit. You can buy a $8 set of barrel vise blocks and $30 Barrel wrench from SharpShooter Supply and change your own barrels.
I just picked up a like new Shilen 26" heavy barrel already chambered and threaded in 6mm BR 1-8 twist for $225 and threaded it on by Savage model 12 BVSS this afternoon.
IMO the 6mm BR is the cheapest and easiest target round for 600 yds and even out to 1k with an 1-8 twist barrel. Death on ground hogs with 87 Vmax also.
The 308 and 6mm BR are both short action, so barrels will interchange on the savages.
Learn to reload and go with a 6mm BR though.
You will not regret it.
If you want to go with the 6mm BR now, then look on www.6mmbr.com
and savageshooters.com at their classifieds and you can always pick one up for $800-1400. Watch the twist though. you want either the 1-8, 1-9, or no more than 1-10.. The 1-8 would be my choice.