For what the OP described, the 5.56 will do. Shooting a crate of ammo won't break the bank.
Alternative calibers are good for the extra power or precision they can deliver, when paper and dirt are primary, then expense is the overriding priority. At that point it's either reload or suffer the cost. NONE of the alternate calibers shoot cheap milsurp ammo - they aren't and probably won't ever be for decades anyway. So, it doesn't help at all to fanbois the flames for one or the other - as the OP noted, .22 got the job done for awhile, and commercial priced ammo doesn't seem to be his focus.
The AR15 is the better choice for now because it's primarily available in a cheap caliber. It's other advantages do play well, you get a widely accepted set of dimensions, most optional parts literally drop in or screw on, improvements in different sub categories have a lot of depth, and it's still the issue weapon and caliber. AR10, not at all. I helped make sure the surplus .308 is all gone, the AR10 actions aren't all the same, which means they become single suppliers with no competition to keep prices down. The market reflects that, a run of the mill AR10 is double the cost. Not to forget, more recoil - .308 is not a fast firing round, the history of the full auto M14 shines there, and weighs three pounds more. Reason enough I sold my .308 self loader of German origins and built an AR15.
If, later on, an alternate caliber is attractive, the ones that fit the intermediate receiver of the AR15 are literally drop in, and assembling them yourself is done more easily than changing a water pump on a pickup truck. Or, buy a complete upper and just push pins, voila, new gun. The joy of the AR is that you can do that.
For what the OP has in mind, I'd go with a conventional fixed stock 20" barrel, something with full rifle handguards and sight length. The A3/4 flattop will let any optic mount, and beyond that, leave it be.