Your .308 should do fine with Federal Gold Medal match.
For long range shooting, choose the 175 grain MatchKing in that round. From my rifle, it achieves 2655 feet per second at the muzzle. On your optic, make darned sure that you have enough adjustment to reach out to the distance you want to go; you're going to need to come up anywhere from 40 to 50 minutes in elevation to put you in the ball park at 1000 yards.
For optics, a Leupold 4.5-14 will give you 100 minutes of internal adjustment; the 16x fixed gives 140 minutes--more than enough to reach out there. The IOR Valdada scopes have excellent glass, and some of their models have more than enough elevation travel--however, in some cases they take non-standard rings.
My favorite are the Nightforce optics--the 3.5-15 and the 5.5-22 have enough travel adjustment, super clear and bright optics, and they're built like a tank.
If you do handload, I have used 41.5 grains of RL15 under the 175 grain MatchKing in new or once fired Remington and Federal cases; on the once fired cases, I trim to 2.00 inches, with a loaded OAL of 2.820. I use Winchester primers, and I have also used the CCI #34 with good results. This is a sub-moa group from my Model 10FP.
Hiding in plain sight...