Hello from Georgia,
I have several .308 rifles and love them all. This is my personal favorite cartridge because of the accuracy, reliability, predictability, versatility, ease of reloading and availibility of ammo. My " go to rifle" is a NEF Ultra single shot but I also have a Rem. 742, Savage 112, and Ruger #1. Each of these rifles has its own preference as to the load it likes.
When trying to decide the load to use, I feel that the rifle should have the last word. Since I handload, I can try a great number of different configurations with the same weight bullet. My favorite is 165 - 168 gr. bullets in Hornady and Sierra with Varget or H4895 powders. The 168 grain bullets seem to give the best compromise of flat shooting with plenty of mass to efficiently take any large game that I hunt. I load everything from 90 grain carbine bullets to 200 grain round nose bullets but have settled on the Sierra GameKing 168 gr. as my hunting choice.
Each rifle is an individual which likely has a favorite load. The fun part is finding which one is best. I suggest keeping a detailed log on each gun for the life of the gun. This will allow you to get to know it's likes and just as important the dislikes. It will also let you find a good "back up " load if you run out and can not find your first choice. I try to find at least a few factory loads that group close to my handloads so that I can simply buy them over the counter if need be. I have found the Federal loads to be a good overall choice when matched to the gun.
Good luck with your .308 and choosing a load and always remember that the single most important factor of taking game is the self discipline to wait for the right shot and placing the bullet in the right spot.
Dave