For the .308, any good 168 grain bullet does well in most barrels. The Army uses the 175s in the long-range cartridge, but my best groups have been shot with Sierra Matchking 168 grain bullets. I've also gotten some great groups from Hornady's AMax bullet. The powder is easy, either Reloder 15 or Varget, depending on what is available. They're both great powders for the .308 and very close to each other in burn speed.
For the .223, it depends. It depends on whether you're shooting a bolt or a gas gun, what the barrel twist might be, and your preferred bullet weight. Lots of good bullets for the .223, and lots of good powders. As it turns out, both Hodgdon and Alliant list .223 data for Varget and RL15, but you might find better propellants based on the bullet size you settle with.