Hi There,
Now before you go plonking down lots of cash for a new rifle, scope and mounts. May I suggest that you check out a few stores and their used gun racks you may just, find the pefect rifle for you, save yourself a bundle.
Personally I would try to shoot as many of my friends rifles as I could and see which one feels the best to me then go looking for one of these. If it's used but in good condition then I would find the best condition used rifle that felt the best and then worry about chambering. .270 win, 30-06 Sprg, .308,7x57 or 7mm Rem mag would all do. Rifle fit to you is as important as chambering as when you need to mount the rifle quickly a good fitting rifle will make all the difference
Good luck on your hunting
and please let us know what you get.