I picked up a T3 stainless synthetic in 308 a couple months ago, but haven't shot it much due to weather. You'll like whatever caliber you get. I see that in some configurations a 7-08 is available, and by now there may be more calibers such as 260 rem or 6.5x55. If so, I hope you'll carefully consider the versatility of these chamberings.
I started hunting deer with a 6mm rem, and had good luck with it. It and the very similar 243 try to do too many things, however, and are generally a bit light for deer and overkill for varmints. They'll do either job with good bullet placement, but don't leave much margin for error. The 25-06 is a little better medicine for deer, but still light for elk or bigger game if you should want to take that up later.
The slightly larger calibers have a greater bullet selection, retain more energy and yet are very pleasant to shoot.
Any of them will work, and I know you'll enjoy the T3. You can't go wrong.