Well... all the usual suspects and all their favorite cartridges
And to join in the fun, I would go with the 300 WSM... surprise
The 215 Hybrid would probably be my first choice of bullet.
Let's look at the two cartridges objectively.
7 STW 92.7 gr H2O capacity
300 WSM 79.3 gr H2O capacity
The STW has about 12% or so more capacity than the WSM. What does that mean?
It can shoot a 180 bullet faster than a 300 WSM can shoot a 215 bullet.
Recoil is going to be very close. Things that affect recoil are weight of rifle, weight of bullet, charge of powder and muzzle velocity. In the case of the STW, it's greater powder charge and MV are going to drive up recoil and with the WSM, the bullet weight is going to drive it up. I don't think you would be able to tell the difference if you were to shoot them blindfolded.
Barrel life definitely goes to the WSM. Less powder through a larger hole and lower MV.
Range.... the STW will have greater range than the WSM... but both are more then adequate to well past 400 yds.
Terminal ballistics... IMO, a toss up to the ranges you are talking about. The STW will hit with greater velocity, but the WSM will deliver a larger cal bullet with more mass to the target. With frangible bullets like the Bergers, more mass and less velocity is a good thing. You might have issues at close range and high velocity with frangible bullets.
The STW is going to favor a slower burning powder due to it's larger case and small cal., therefore it will need a longer barrel than the WSM for efficiency.
I like the WSM because it will deliver a bigger bullet at a good velocity and it will have better barrel life and I can use a shorter barrel.
The 300 WSM likes RL17 and I have shot 210 VLD's out of my 24 3/8" barrel @ 2930 over RL17. If you prefer a powder like H4350 or 4831sc you should easily get 2800 plus with 215's in say a 26" barrel. In a 25" barrel, I would think you easily get 2950 plus with 215's.
I agree, that you should go with AT LEAST a magnum sporter contour, and no fluting, for stiffness.