Tikka T3 in 308. Don't worry about recoil in your hunting rifle, you are only going to get one shot, and then the deer is running. While you're sighting it and training, take your time, if it's only 10 per session, that's ok. You typically have 50 weeks to get ready for season.
I used to love being able to hit hard at 1000 yards. As I get older I find hitting a mini ram at 200 yards with the 22 oddly more satisfying.