Heavy Edit on this Post.
Alex, the .338WM is a very capable long range round. I have a burned out barrel on a sporter rifle to prove it. Why? Because it was all I had at the time. I have moved on to, what I consider, better things, as most will, in time.
Truth be told, almost any round, and rifle configuration, can be capable at long distance, and this has been proven over and over again. The 375 H&H comes to mind, as do many of the others mentioned on this thread. Mount a turret adjustable scope on most anything decent, and you can shoot and kill at distances well over 500 yards. The most specialized equipment for doing this, is between your ears.
Another truth is looking at and quoting energy numbers. They don't mean anything, so stop looking at them and quoting them. Look at the velocity numbers instead, they mean way more.
Recoil can be mitigated in two ways, one can add weight, or twist on a brake. This helps you shoot more, flinch less, and become more accurate. When done correctly, big boomers kick no more, or less, than little boomers. If one is concerned about costs, and looks, and noise, and all of the other bad things that come with a brake, then add weight. It is also cheaper for the shooter with money on his mind, which seems happen here quite a bit.
As far as purchasing ammo is concerned, most serious long range shooters would just not do this, as it is not fiscally responsible, or possible. It takes a lot of rounds to become consistently accurate at distance (again, over 500 yards) and, as I personally found out last year, there are no shortcuts, and no substitutes for practice.
Bottom line, invest your shooting dollars with a mind to the future, and become proficient with what you have, no matter what it is. Buy the most LR scope you can afford, and slap it on the rifle you have. Go out and shoot, and shoot some more. It isn't rocket science voodoo witchcraft, but it is an expensive hobby. It is a lot like racing cars, if you wanna go fast, you gotta spend money. If you wanna shoot more and more accurately, and constantly improve, you gotta spend money. Get to reloading, as it costs less that buying ammo, and the more you do it, the cheaper it gets.
And God knows, on these forums, it always seems to be about cheap.
R.