so when I built mine
Trigger - triggertec adjustable flat trigger, it's crisp, light, easily adjustable, and so far dependable(zero regrets)
Barrel (need a length too because I'm dumb) - I went with a 20 inch, 1:8 twist, 223 wylde chamber, custom made by ATRS in the thickest profile I could get. the god eugene stoner designed the AR and the gas system to work with a 20 inch barrel. If he designed it for a 20 inch barrel, who am I to question him?
Bolt Carrier Group - Lantac, it's coated with the souls of children to reduce friction, fouling and stoppages (and it's silver, so it looks all purdy through the ejection cover). It's been reliable, and when I've been lazy and run it dirty and dry, it's still been reliable, so I'm happy)
Hanguard (free floated obviously) - I went with a seekins precision sp3r, it has 5 sides, and gives me a LARGE flat bottom, for shooting off barricades and it is very solidly attached (and leaves my gas block adjustable without needing to remove the rail), no regrets
Gas tube - cheapest one I could find in the correct length
Gas block - adjustable, tuned to the point where it locks open (always) but the buffer doesn't slam home. It ejects so reliably you could set your watch by the ejection pattern.... crap, I don't remember the make, but I got one with detents and with the nut on the front so I could get to it under the rail. I could never own an AR that doesn't have an adjustable gas block as most are way over gassed
Buffer kit - just a regular/stock rifle buffer (not a carbine buffer), I considered the jp enterprises silent buffer for tweaking if needed (but it is not needed)
Stock - Magpul PRS. I looked in to the luth-ar stock, and it didn't look solid. I find I prefer my gear to feel solid, and I am ok with the weight. the Luth-ar might be solid, I just wasn't interested in taking the risk so I went with "old faithful"
Lower parts kit - I used a daniel defense lower parts kits, but honestly, just about any LPK would do. If I were to do it again, I'd buy the cheapest lpk without a trigger and grip
Charging handle - radian raptor, IMO the best there is...
Before going down this road, I'd consider an non-restricted build, for me, I WANTED an AR, but it would be nice to take something out to my friends land to plink away at 600 yards. as for the 224 round, it seems pretty interesting, but the bigger concern is where can I shoot it? inmy area, the only longer ranges are military ranges, and they aren't all approved for "new" cartridges. Petawawa for example is approved for 223/556, 762 nato/308, 303 british and 338 Lapua I believe. So if I tossed a 224 valk barrel on, I couldn't take it to those ranges, and would be stuck at 300 yards. So do some homework before commiting to an AR build, and the caliber.
Good luck, and have fun. Building an AR is fun