Got a PSS in .308 and a .300 custom Model 70. Recoil sensitivity is a big variable.
The .300 is a 15 lb. rifle, but I had no issues with banging 60-80 rounds a day through it from the bench. The Vais brake will work if you feel the rifle is beating you up too much.
Of course, a few of us think that offhand plinking with a .375 H&H is fun, too!
Practically, the .300 will extend the range you are able to reach out and touch a target by 200-300 yards, if you do your part. It will take more $ in bullets, powder, brass and loaded rounds to get there. The decision as to whether it is worth it for you is yours.
The .300 WM PSS is a nice rifle. It will be a good beginner's benchrest rifle for punching paper, or for building a long range precision rifle. It is not a particularly good rifle for deer hunting, as it is long, heavy, and more cartridge than most N. American deer require.
I agree with the Leupold scope choice, and would recommend the 3.5-10x LR M1 or M3 for this setup, if intended for tactical use. If you are going to be doing nothing but paper punching at extended ranges, you may want a fixed power model. Concur with the Badger rings and bases comments.
Just my .02, YMMV. Hope this helps.