As a former Army SF Weapons Sergeant (MOS 18B), I carried an SOP small AR/Pistol weapons parts kit to the field. I used a standard USGI nylon ALICE cleaning kit case for that purpose. It held nothing else but small gun parts and a few small tools (brass/nylon hammer, micro needle nose pliers, drift punches, screw driver set, mini hex/torx bit set for optics or gas key, jeweler's files, Leatherman tool, emory cloth, armorer's wire, spare Aimpoint optic battery cap, pressure tape pad & cable, weapon light bulbs, ruptured cartridge extractor, AR wrench, etc.). I was expected to complete minor fixes and repairs to detachment weapons while out on the ground. Which meant that I carried a few small spare parts for pistols as well.
All of that stuff fit inside that 3-snap pouch. I maintained a second pouch for my personal weapons cleaning kit.
In small zip-locked parts bags (pill bags), I carried complete AR small parts & spring/pin/detent kits, plus one entire BCG (ready to fire), and a new charging handle assembly. Besides parts for a trigger housing / fire control group, I had a few spare front & rear sight parts, gas rings, and replacement screws/washers for things like optics, rails, pistol grips, or fixed butt stock. I carried no spare furniture or other larger items like buffers, buffer springs, rail components, optic mounts, or slings. Just small stuff. The two biggest things were the BCG & the Charging Handle Assembly.
Honestly, I rarely had need for any of it, as our AR pattern rifles/carbines (M16A1, M16A2, M4A1) rarely failed. The most common occurrence was some team mate dropping & losing a tiny part while he had his weapon disassembled. Try finding a tiny missing pin after it's fallen into the forest floor in the middle of some MSS (Mission Support Site) or patrol base. Even that was exceedingly rare, 'cause guys take meticulous care with their bullet launchers. An upturned patrol cap or boonie hat is a good location to place disassembled parts.
I carried a separate spare AR firing pin but can't ever remember needing it.
Thus, based upon my observation of hard use guns over the years, the 3 most critical AR parts (or assemblies) I'd carry would be the ones most likely to go down while firing or get lost by some cone head during disassembly:
1. 1 x complete Bolt Carrier Group (Bolt, Bolt Carrier, Firing Pin, Extractor & Ejector)
2. 1 x complete (2nd) Extractor Assembly (extractor, spring, spring insert, retaining pin, & O-ring)
3. Spare BCG Pins: 1) Firing Pin Retainer Pin (bolt carrier cotter pin) & 2) Extractor Retention Pin. A couple of each.
Next most likely culprits for replacement would be replacement screws for mounted accessory optics & bulbs or O-rings for combat lights.
Over a decade ago, I purchased a DPMS-made AR field repair parts kit that includes the most likely (but only infrequently) needed small items. I've yet to dip into it, but it's piece of mind for not a lot of money. Similar to this one:
DPMS Firearms | Remington Outdoor Company
I agree with buying premium parts when it comes to spare BCG for a defensive weapon. BCM or Colt components are what I choose to use.
Just my $.02 & I hope that helps...