RE: New .308
I would suggest to start with the same bullet that you shot from your 270. If you liked BT's, Partition, Accubond, or regular Pointed Soft points, loaded by Winchester, Remington, Federal or whoever. I would stick with what you have confidence in. If you get exceptable accuracy, you're all set and ready to go. If not, there are dozens of others to try. Any common bullet weight from 150 - 180 gr.will flatten deer out to 300 yds and beyond.
I love my A-bolts, I'm sure it will prove to be a fine rifle for you.