If you haven't already read it, I highly recommend the article here on Ric Horst's long range hunting rifle, a 7mm WSM:
http://www.6mmbr.com/gunweek064.html
I've used the 7mm Rem mag quite a bit over the years, it's a wonderful hunting cartridge. Recoil seems about the same as a .30-06 to me, in other words, it's just a peach to shoot. With the larger 7's, like the RUM or the STW, I'd probably want a muzzle brake.
Nothing wrong with going with a magnum for a hunting rifle. It adds some muzzle velocity, which is a good thing in a hunting situation.
One shot, a mere 180 yards, at nearly 10,000' with a decidedly low budget 7mm Rem mag. I was using 175 grain Nosler Partition handloaded to about 2900 fps from the 24" barrel. The 7mm Rem mag has a wonderful history of taking western big game for the past 40+ years, and the 7mm WSM produces very similar ballistics.
Take your pick, I'd choose either the 7mm WSM or the good old 7mm Rem mag. Likely the 7mm Rem mag as it's well known to me. Both are accurate, easy shooting, very lethal hunting cartridges. Lately I've been working quite a bit with the .300 WSM, and have grown fond of it. I'd suspect that the 7mm version might be even better for general purpose hunting. Have to admit though, that I do like that big 210 grain .30 cal Berger VLD.
Oh yeah, just remembered, there was a young guy hunting with me last fall who saw a bear come over a ridge not five minutes after I'd shot mine. We watched the black sow come down the ridge, and I ranged her at 504, then 485 yards. Chris dialed his scope for 500 and planted a 140 gr Barnes TSX into the bear, breaking her spine and sending her tumbling down the ridge. He then followed up, and came upon the wounded, ticked-off bear, at about 10 yards.... He finished her off with a couple of very rapid shots. It was impressive performance both from a young hunter and from the 7mm Rem mag. Just a factory built sporter rifle, a Remington as I recall, but I could easily be wrong.
The 7 is capable of superb accuracy and great performance on game. I'd say that goes from whichever case you choose to use. Somehow I'm most drawn to the .280, .280 AI, the 7mm Rem mag, and the 7mm WSM. The smaller cases are okay, but why? It's a hunting rifle. Might as well go for power. The bigger cases are okay, but why? If I want more power than the 7mm Rem mag or the WSM I'd just as soon go for a .30 cal or larger.
Regards, Guy