I've got a 7 RUM in a Remington 700 Sendero SF. Probably the best shooting gun in my collection. It's not a carry-around gun with the bipod and big Sightron SII series scope but it does shoot nicely.
As for 7 RUM vs. 300 RUM. I asked myself this question before I decided and opted to go with the 7 RUM for the simple reason that it shoots marginally flatter and it would probably see more use on long range whitetails than big game. The 300 RUM is a favorite here as well though. I don't think recoil is a problem but then again it isn't a sporter weight like you're talking about. Actually, if you're looking for shooting around 300-500 yards there's many other magnums that would work just as well, with less powder and recoil to include the 300 WSM
, 7 Rem Mag, 7 WSMand many others. Of the other choices, I'd probably consider the 300 WSM. Plan on doing LOTS of range time and reloading. Get your trigger down to something light, a high quality (i.e., $300+) scope from Leupold, Sightron, Nikon, etc. and have at it.