I've built two, an AR rifle in 6.8, it ran over $1,100 with the best possible barrel, bolt, and carrier on the market at the time. The next was an AR pistol in 5.56,. I spent the absolute least I could and it ran under $600 cherry picking special deals and parts some wouldn't touch with a ten foot pole - but it works just fine.
Of the two I shoot the AR pistol more simply because I can feed it Tula steel case at 7.99 a box and they go bang every time. Surplus about the same. The 6.8 - and .300BO, and 6.5, and all the others - will never be that cheap. Commercial ammo runs higher, except white box, and because ot that I can shoot 5.56 twice or three times as much for the money than a specialty commercial cartridge that isn't available as battle packs sold out of old inventory by governments getting rid of those lot numbers because it's too old.
Having shot my share of .308 in the day a 24c a round the lesson stuck with me. The 6.8 is a dedicated deer rifle, I might use up a box or two a year. The AR is the trainer, I might use up half a dozen at a range session. There is the best reason to go 5.56 if doing your own build, the second is that most of the parts are all compatible with 5.56, and therefore cheaper. A speciality barrel and bolt can run up to $399 - like, .375 SOCOM - and there may not be any other reliable choice in a certain cartridge as only one or two usually finesse the best performance out of them. The rest are all commodity grade with feeding, chambering, and extraction issues.
Then you get into the other required parts, like bolts and magazines, as different cartridges aren't the same dimensions, may not be strong enough, may not have the magazine ribs spaced correctly, or the front of the mag cut away, or curved to match the taper of the cartridge. That also brings up the stock straight magwell of the AR15 and why some conversions just aren't reliable as tapered cartridges attempt to rattle up the chute to be loaded. 6.5 has that issue, and the final solution is to use a special lower and bone stock AK mags to make it work correctly.
As for wrenching your own, you don't need a long laundry list of tools - many of those recommended aren't even in the armorer's tool kit as that is built to service unit firearms from pistols to machine guns. It's not AR centric, and it's also set up to keep a twenty something unit armorer from twisting off parts, ruining threads, or attempting repairs that Army states should be sent to depot. Unit armorers rarely if ever replace a barrel, it goes up the chain. It's guys like us who do it making an AR or taking it apart to change it up.
Two cases during the assembly of the AR require something different, one, inserting roll pins, which are either flat springs wound into the shape of a small dowel, or the thick kind that have a long split down one side. Avoid the latter in parts kits, get the flat wound spring kind which insert 10X easier. Use a pair of vice grips with taped jaws and they press in easily. Us a hammer and roll pin punch, you will remember doing it wrong every time you see that dent on the side of the lower or upper. Second, torquing the barrel nut, which by the official -10 is not actually torquing it at all. You are tightening it to over 30 lbft and then going a tad further to clear the teeth to insert the gas tube thru the hole in the upper. The instructions specifically state not to exceed 85 lbft. Its not a torque TO specification, it's a DO NOT EXCEED specification. Much like saying torque lug nuts to 110 but do not exceed 250, and for the same reason - you will strip the threads. Over 30 and pass the gas, it's good.
For much of that a bench vise with rubber jaws or a mag insert holder will do, your choice, spending money on tools should be part of a much bigger dedication to general repair. And understanding what you are doing counts, I torqued my barrel nut with a pair of 18" channel lock pliers, done. Gun worked fine. Tore it down to change furniture, had the "armorer's tool" that isn't issued to anyone, it's commercial, and after the teeth slipped the barrel nut was still no worse for the wear. Those tiny studs don't grip that well when you are hanging off a torque wrench and get sideways.
As advised, buy a complete lower of choice, upper of choice, and you pin together and shoot. It's cheaper because you aren't buying all smaller parts at retail, and neither do they - plus an incomplete firearm doesn't pay the hunting tax surcharge of $80 a complete one does. Add in that if you did buy all the little stuff from a lot of different vendors, you then pay half of dozen or more shipping charges at $8 -12 a whack. A stripped lower also has to go thru an FFL who will charge $25-40 or more to book your transfer, check fees before you order. My 6.8 had over $140 in processing and shipping fees involved. And then I swapped furniture on it and added more to the overall cost.
There is a related issue with building your own AR - those parts left over if you have any from ongoing upgrades. Some buy a complete upper or lower with the idea they will swap a stock or put on a different handguard which drives costs up. Selling the parts, sorry, they are used once installed, and nobody will pay retail As those parts accumulate you then keep them in a box in the dark, and after a year or so, the fumes keep getting in your head, and they hatch an idea of another AR to build, using them.
I'm now acquiring the specialty parts for another build, since I have furniture, buffer tube, buffer, spring handguards etc all poking me with a long stick. That is known as Black Rifle Disease, the final product doesn't have to be all black just like variants get other names. In our case, tho, there is no vaccine. It's incurable, it only takes a few parts and a specialty tool sitting there murmuring in your sleep about the latest new cartridge, how you missed that deer two years ago, what if you had something bigger that shot a 200 grn .375 with 55 grains of powder behind it . . . .
And down the rabbit hole you go, again.