Hi tctt3,
Are you certain that you want to go with a .300 Win Mag? I've fired one from a bench. It did recoil, more so than was comfortable. But that's my take. Yours will probably be different.
Based upon what you intend to hunt and the ranges you intend to hunt, I'd recommend a .280 Rem. But that's they way I'd go, which might be the wrong way for you. I hunt with a 7MM Rem Mag and a .270 Win. I have made long shots on deer and antelope with each. They will kill game at very long range. The 7MM Rem Mag is the most powerful hunting cartridge that I can shoot from a sporting rifle off a bench without recoil becoming an issue. Even a .308 Win will satisfy your criteria, and it won't hurt to bench shoot all day long.
As far as guns go, my first choice would be Sako, but that'd set you back at least 2 grand. On the upside, Sako guarantees five-shot MOA, which means you won't have to invest to make it accurate. From experience, I can tell you that Sako rifles are beyond extremely accurate. My second choice would be this one:
Tikka T3 Hunter Tikka guarantees three-shot MOA. I have yet to read a negative thing about Tikka.
I'd suggest doing a lot of research. Try to shoot your friends' rifles to find out which is right for you. If you have a friend who owns a .300 Win Mag, buy a box of ammo and put twenty rounds down range. If recoil is manageable, then that's the way you ought to go.
In the end, it will be your rifle that you'll hunt with. So you'll have to go with a gun that's right for you.
I wish you many successful hunts.