Varget would be my first suggestion... it works really well for a lot of people. Given that it is just about unobtanium (again) in light of recent political events... it may not be viable.
Both I/H4895 have their adherents, as do Viht N140/N150. You don't see very many people using N135 with bullet weights suitable for long range competition... but thats not to say that nobody does or that it won't work. Just that most people looking for a powder at the faster end of the burn rate go the 4895 route, or occasionally 8208XBR. I've used RE-15 with acceptable results in the past, but outside of people looking to reconstruct M118LR sniper ammo, you don't see it used a whole lot in LR .308 match ammo.
Lapua cases are my first, second and third choice. Winchester if you're tight or if you want to run really hot loads and feel you need the extra boiler room. Plan on doing a fair bit of extra sorting/culling to get them up to the same standards. If you already plan on neck-turning and weight-sorting, then it may not be an issue for you. My experience with Winchester brass is that when properly prepped it can shoot *very* well... but getting there is more aggravation than I'm interested in. YMMV.
With the 12 twist... should be able to run anything from 155s to 190s easily. Either the Sierra 155 Palma (2156) or the Berger 155.5 BT Fullbore are excellent bullets and should shoot well over 46.5-47 gn of Varget or N150 in a Lapua case, lit by 210M primers. 168s in general... if there are any plans to shoot beyond 600yds, I'd do yourself a favor and skip these. Some work all the way to 1k, some don't, no matter how hard you drive 'em. Best to just avoid them. SMK 175s shoot pretty well, as do the Berger offerings. IIRC, that gun probably has an Obermeyer chamber in it, which is good... other than the throat is a tad short for the heavier LR bullets. As you start going up into the 185-190+ range, you may find you have to seat the bullet far enough down in the case that it starts eating away at the case capacity to the point where you don't gain much if anything over a lighter bullet going fast (like a 155.5BT @ 3000fps). That can be gotten around, to some degree, in some instances, by experimenting with other powder choices. Alliant Power Pro 2000 MR is a newer, much under-advertised, high density powder that is a bit slower than Varget, but a bit faster than say H4350. Seems to work well with the 185s from my factory Savage 12 BR barrel (same chamber), netting surprisingly high velocities with ease.
HTH,
Monte