Old thread, but since I'm new, figured I'd chime in with my .10 since I have had a long standing love afair with a .300 WM.
I built a custom .300 WM over 20 years ago for just what you are talking about that I have subsequently "shot the hell out of". She never was one that could be called beatiful, but she was always there and unfailingly reliable for the hard work. That rifle used to be my most accurate and would routinely hold under 1/2" with about anything I fed her. Now she's old and tired and in need of a new barrel. Just not sure if I have the heart to do it just yet.
I have no idea how many rounds I have put through her, has to be several thousand, but she has never failed me nor the many others that I have loaned her to in a hunting situation. Most every time when the trigger was pulled, the critter on the other end fell over with one shot. That gun has been a go-to for numerous elk, mule deer, whitetails (coues and plains), antelope, hogs, javalina, and turkeys. I even used her hard on numerous fun filled days of long range prairie dog and rock chuck shooting.
You absolutely can not go wrong with a good shooting .300 Winchester. Best thing you can do with any rifle is get a good trigger - particularly for a big gun that you want to shoot long range with. I put a Timney on mine and it is sweet. I would strongly recommend putting a muzzle break on a .300. My rifle has a break and it really helps the recoil. Most times I actually see the shot hit on game which is pretty cool. They are hard on the ears, though. I would recommend always shooting it with hearing protection. I am pretty sure that some of my hearing loss can be directly attributed to the break.
For your best efficiency and velocity with this round, you should get a rifle with a 26" barrel. If you are serious about accuracy and consistancy, get a good wood or synthetic stock (not just cheap plastic) with the barrel floated, aluminum bedding block and glass bedded action. There are several good factory guns out there that fit the bill with a minor amount of work - I am kind of partial to the Remingtons.
All that being said, there are a number of great rounds out there that will be more than adequate. The 7 mm Remington Magnum, in the right gun, will outperform the .300 WM at your longer ranges.
I am kind of partial to the 7 RM without a muzzle break because the recoil is much less than for the .300's and the accuracy that I have seen has been exceptional in most every 7mm that I have ever shot. The guys over at "Best of the West" use the 7RM for most all of their ultra-long range shooting and have multiple one-shot kills on elk and deer at 1000+ yds. I have shot and have seen shot a number of elk with a 7RM and have also been quite impressed with the killing power of the 7. I know several guys that have killed piles of elk and mule deer with a 7 RM over the years that would not use anthing else.
Basically, you can't go wrong with either the 300 Winchester or the 7 mm Remington. I would opt for the 7 if I had to pick one these days just taking the recoil issue into account. Would not hesitate to shoot anything in North America with a 7 RM, short of a brown bear in thick cover where I would prefer a .375 with open sights or a very low power scope.
Hope I didn't confuse you on the issue. Should give you some more to think about though.