"Best" is subjective and should be accounted for on a per-situational basis. In other words, hunting coyotes with a .338 Edge just MIGHT be a bit overkill...
But it's still a blast!
I'm a big fan of the 338 super mags. In my experience, recoil is relative to the platform, and once a shooter applies the effort to learn a platform, then said shooter should be able to become proficient and consistent with shooting stamina and endurance. Muzzle blast is a different thing all together, but is negligible because of hearing protection. Can they be expensive? Yeah, I suppose. I see 338 LM ammo on shelves for $65-$80 per 20 rounds. Two years ago those same boxes would've been $120+. The RUMs are definitely cheaper. Really, though, if a person isn't rolling their own in this sector of shooting then they're doing their self a disservice.
The 6.5 craze hasn't hit me really. I've entertained something in the realm of a 6mm-6.5mm cartridge, but they can't do what a .30+ magnum can. It's a marketing thing, and I can't buy the manufacturers' sales line, especially when the 6.5s do perform at half the capability of larger super mags.
The 7mm magnums are great. I know lots of guys that shoot a 7RM. They love it, and they kill critters. They don't hit with the same force of some other rounds, but that can be compensated for with the right projectile for the job (which I think is something people overlook in their search for "best caliber" or "best cartridge").
I know my logic sounds like
the bigger the better! The truth is that a person needs to pick the best caliber, cartridge, AND PROJECTILE for their situation/needs. Some things won't be as "practical". It's not "practical" to shoot prairie dogs with a 338LM, but I still do it. Just like it's not "practical" to shoot a buck mule deer at 420yds with a 62gr core-lokt out of a .223, but I still did it.
I operate with the perspective that there are different tools for different situations, and therefore, I have rifles for different scenarios. It could be different for somebody else. So, run with what does and what will work for you.