I would go with a Ruger M77 Mk II, it is very hard to beat a Ruger for the money. I have the 77 all weather in 300 WSM and It will shoot a .6" group with my hand loads. I would recommend that you get a 30-06 because it has the largest bullet range on the market (55gr to 250gr) and factory ammo is cheaper than most other calibers and it can be found in any small sporting goods shop in the country, in case you go on a trip and forget your ammo. The 30-06 will kill anything on the planet out to 300 yards. If you do decide to go with a magnum the 300 WSM can be handloaded faster than the 270 and 7mm short mags and Weatherby mags with the same bullet weight, but I am am not sure about factor ammo so you should check on it.

If I could only have one rifle it would be a Stainless Ruger 77 in 30-06.

I would stay away from the 7mm RUM because last I knew Remington only loades one bullet for it (140gr B-tip, I think).