As far as deer calibers, the .308 and 30-06 will do just fine. The 30-06 probably offers the most variety of bullet weights for factory loads. I have also killed a number of elk with the 30-06. The 300WM is another fine choice for elk.
Not sure what your budget is or how much the Remington goes for, but check out the Weatherby Vanguard Series 2. It is very accurate and I picked one up in a 300WM for $500 new from an online gun shop out of Texas.
Good luck.