Probably a 180 gr Sierra MK. Some guys shoot 190's, depending on the cartridge. I think Lilja's website has a link to a twist calculator. You might look there or do a search for a rifling twist calculator. You will need the length of the bullet in question, the weight and the ogive profile, plus the the velocity on most calculators. You might also do a search for the Greenhill formula.
Jerry's right. I've personally shot 200gr SMK, 210gr Berger's, 190gr JLKs, through a 12 twist 30" barrel chambered for 308 Baer. They all shot really well with those higher velocities.
We also shot 220gr SMKs with the original lot# of R22 when it first came out (much slower then today's R22 powder!!!) and they stabilized on our 400yd test range. But that load was really really hot. Never shot that again. Wrecked the cases doing it.
I don't have any experience with slower 308 Win or similar velocities in a 12 twist. Anyone with a Rem 700 Varmint Special should be able to tell you. Those barrels are 12 twist from the factory for the 168gr MK.
I wouldn't recommend the Greenhill formula. It's old and based on a drag function from bullet shaped/made 100yrs ago. With todays bullets it usually recommends a twist that is a 1 or more inches faster than needed for stabilization. That has been my experience with 6.5 -> 338 modern day boattial bullets anyway.