It's really a matter of balancing strengths and weaknesses. Each of the calibers listed has strengths, and each had to trade away a certain amount to be more optimum in one category more than another.
In terms of ballistics, it's a simple fact that the overall length creates a window of performance, and it can't be escaped. There's only so much room to stuff a cartridge full of powder and leave enough room for a bullet to properly seat. After that, you get into modifications that mean having non-GI parts - usually barrel, bolt, and magazine. Lately "new" cartridges have been introduced that only change the barrel - what offsets that is only the vendor is a source of ammo. In most regards, it won't be on the Boxmart shelf at all, internet ordering of ammo will be required.
Cost of ammo is no worse than any other commercial round, and comparing commercial to milsurp or NATO reject is ludicrous. Military surplus is the EXCEPTION to normal ammo pricing - not the standard to compare to. Those who make that mistake like to shoot a lot of dirt or paper, and won't reload. Since only the 5.56 will enjoy cheaper pricing, don't let that get out of focus - FMJ import ammo isn't your best choice in hunting rounds, and that means we're right back to conventional soft point or hollow point costs.
Caliber IS important when choosing what elements you pick: In diminishing order of available supply, 5.56, 6.8SPC, 6.5G/.264LBC, then The Others fall into place. These all enjoy the biggest share of the AR15 market. If 5.56 isn't legal or desired, moving up to the 6's will improve power 40%. 6.8SPC was designed and optimized by the SF to shoot full power from a 14.5" issue length barrel, and does great from a BATF legal 16". MOST 6.8SPC shooters do exactly that. 6.5G has a slower powder burn and enjoys a longer barrel in it's optimum form, many use it in shorter ones and are successful - but give up the advantage of the better BC and longer range by the 4" or more shorter barrel. When you're limiting the range to 250m or less, it won't make a substantial difference, and the trajectory on equally loaded rounds is less than a candy wrapper at the longer ranges anyway. It will take a good optic and experience calling bullet drop to notice it.
Once caliber is sorted, then the features fall into place. The barrel length dictates gas length, mid length or rifle are the most available choices. An A3 flattop for optics, fixed length stock (half the price and has worked for decades,) grip in your size, and then what fore end? Lots attempt to justify a free float, unless you have deliberately bought a high precision 1MOA or less barrel, it's not needed. The extra $150 could easily go into ammo and more practice shooting offhand, a better barrel, optic, or another least needed item, a match trigger. Keep the pull above 4 pounds, in field use they are safer when dragged through underbrush or when they casually fall over when leaning against a tree while you fertilize another. A trigger travel adjustment screw is far cheaper and nets 60-80% of the improvement in reduced creep and grit anyway - exactly why so many hunting and target triggers on bolt guns have them.
Since 6.8SPC offers a lot of off the shelf availability, even ammo at Cabela's, Academy, and others, it leads the pack as the #1 alternate. If reloading or fireforming brass is appealing, the 6.5G is habit forming, especially in long range recreational use where the BC makes a difference. And if 5.56 is legal, it can be used, keeping in mind that hunting loads are what get used in it during the season, and they are priced normally right along with any other NATO caliber in a soft point.
I built a 6.8SPC with AGP lower, LAR A3 upper, A1 stock, TD grip, rifle length handguards on a midlength gas 16" barrel. Just ordered an Armalite clamp on FSB to finish it, and plan shooting it soon. It will do ok for hunting, ARP barrels are reputed to be 1MOA, which is a 4" group at 400m. Plenty accurate enough, most alternate calibers will do the same. A 5.56, not necessarily, if it's a run of the milspec barrel. That will cost more, making the build nearly equal in cost to get equal accuracy. Don't make the mistake that 5.56 is necessarily cheaper - you fall into the same trap that surplus ammo shooters claim.
Choose one, check out the availability. It's nearly too late to get a barrel on order and have it shipped for this years deer season, be flexible in how that works out.