If you are only punching paper, something in the 155-175 grain range would be good as far as bullet weight goes. As for what bullet, you need to see what your barrel will shoot best and go from there, as they are all different and no two barrels like the same thing for the most part. But the Bergers, A-Max's, SMK's and even Nosler BT's will all shoot well in certain situations. Do a bit of research and see what you would like to try and find maybe 3 bullets and see if you can make one work. More than likely, if you choose good bullets, one will work out well.
As for powder, again there are quite a few that will work depending on the bullet weight you choose. Varget, BL-C2, H4895, Reloader 15, as well as a few others will all work well. Read up a bit on the advantages of some of the applicable powders and see what you want to try and go from there. You may need to try more than one powder as well, as again, it's a matter of finding what your rifle will shoot best.
You may want to look at the .308 Cartridge Guide as well. It has a lot of good info and explains much of what works with the round in detail.
http://www.6mmbr.com/308Win.html
I shoot a .308, but not as far as you plan to go. I use Winchester brass as I find it to be of excellent quality and very consistent, and if sorted and neck turned, it can even be comparable to Lapua in some regards.
I shoot several different bullet weights and cast bullets as well as jacketed, and have used a few different powders including Varget, H4895, BL-C2, Reloader 15, H380, Win 748, and even H4350 for 225gr loads as well.
Finding the optimal bullet and powder for your gun is really something that only you can find and nobody can tell you what will work best. Find 2 or 3 different bullets that you would like to try and think might work and go from there. Try to keep it as simple as possible during testing and you should have a good combo sooner than you think.
Good luck
Kenny