I have owned 300 Win Mags in Winchester M70s, Remington 700s, Vanguards, Commercial Mausers,
Rebarrelled P14s, and probably others. All were good shooters, and the chambering is quite capable
of handling anything in North America.
It's no secret on here that I like the 308 Norma Magnum best of the "big" 30s. Ballistically, it is so
close to the 300 Win Mag that any difference can be ignored. I have owned at least one 308NM at one
time since 1967, and 600 yards is a realistic distance to shoot with these..
For the OP, I would suggest he find a Vanguard S2 in 300 Win Mag. These tend to be very accurate
and are stocked so as not to beat the snot out of you. [Tikkas tend to deliver more "felt" recoil]
The Howa is the same rifle without the Weatherby stock, so also a good choice.
The Brownings suggested are also good, accurate rifles, but I have not warmed up to them. You may
feel differently when you shoulder one.
Comment on the 300 WSM. Owned 2, both Vanguards. My BIL still owns one of these. Components
less common than 300 Win Mag, and in handloads, gives up about 100 fps. Factory loads [When you
can find them,] are ballistically similar to 300 WM. Both mine were very accurate. Dave.