Well that paired with what you've read about 6.5 doing best in 20+" barrels?
.308win hands down, especially given how much 7.62x51 in the world there is.
No, it doesn't. Few factors:
(1) .308 for some reason took an extremely hard hit in recent buying frenzy. Here's some context: about a week before shit hit the fan with the 'rona, I bought a bunch of PPU M80 at exactly fifty cents per round. Now, the cheapest source for that same ammo is sixty cents per round.
(2) Surplus 7.62 NATO is out there but not in massive quantities. There's Lake City, 1980s Hirtenberger, Malay L2A2, PMC 1980s surplus, GGG, and whatever else you can find kicking around for sale by private sellers:
(3) In its mil-spec loading, like M80, 7.62 NATO is unnecessary as a rifle cartridge. Too much power for not enough benefit, arguably, with substantial detriments such as flinch-inducing recoil for the unaccustomed and barely any control in full-auto. The advantage of .308 is barrier penetration and long range for machine guns. As an infantry weapon, which a DMR is, the .308 is too much gun for most applications. The .308 exists because of US Ordnance's path dependency with .30-caliber cartridges.
For someone getting into these calibers as a newb, I don't see
that much benefit to .308. Though either way, I advise handloading.
308 18"
6.5 20 or 22"
16" is pointless
The advantage of a 16" .308 is that its the shortest legal length of a rifle before SBR territory. This matters when running around stages, or in the woods, or jumping out of airplanes. For example, one of the FAL Para variants had a 17.something inch barrel, which makes sense if you're jumping out of a Dakota into the jungle or brush with a FAL. For a DMR-style gun, though, where you're shooting from a bench at paper targets, a 16" barrel .308 generates excessive muzzle blast unless you're shooting with a suppressor. Which, again, is illegal in Mass.