You can build one for a lot less than $800. It just depends what features or specs you want.
For starters, I'd prowl Palmetto State, Delta Team Tactical etc looking for uppers and/or kits.
Second, you can either build a lower and buy an upper, or you can buy an entire kit. If you buy an entire kit, some will include pre-assembled uppers, some will require you to build the upper as well. My suggestion if you haven't done this before is to assemble the lower but use a complete upper.
For legal reasons, you cannot put a stock on the gun. You can use a normal carbine tube with no stock. But, most people use a pistol tube, which is like a carbine tube except without the six holes for 6-position carbine stocks. You can then optionally add a brace, for example, KAK Shockwave. It may be economical to buy an entire KAK pistol kit, which would include the buffer spring, tube and brace. Expect to pay about $65 or $70 for that kit.
You'll pay $40-$60 for a stripped lower (more if you want a particular brand name) and $40-$50 for a standard lower parts kit. Note, these are standard, not unique to .300 BLK. In other words, the exact same lower and lower parts kit work for 5.56 as for .300 BLK.
You should be able to find an upper for $250-$400, depending what features you want and if it includes a BCG and CH.
If purchased separately, expect to pay about $80 or $85 for BCG and CH. It uses AR-15 standard stuff for those parts.
It will use regular AR magazines. If you have a 5.56 AR, BEWARE. It will ruin your day if you put a magazine full of .300 Blackout in your 5.56. I use 20-round plastic magazines for .300 Blackout for this reason, to make mixups very unlikely.
I personally like the Magpul AFG-2 for pistols. Note, there are legal issues in using a vertical grip on an AR pistol. The angled grip is legally ok. That is my understanding. I am not a lawyer. An AFG-2 and the rail to mount it on should be $35 or so.
And the only other thing to add would be if you want a red dot, flashlight, laser etc.
Not scrimping and using realistic guesses, you can build a nice AR pistol for under $600 easy. If you did scrimp, you could go lower than that.
The ONLY unique part for .300 BLK is the barrel. Well, the gas system is a little different. Literally every other part of the gun is the same: lower receiver, upper receiver, BCG, buffer tube setup etc.
Building an upper can be a bit of a challenge without special tools and I don't advise it if you haven't done this before. But, anybody can pull up a youtube video and build a lower with regular-guy tools and an hour or two. There are some tools that make building a lower easier for one person (the right kind of punches for the pins, a magwell piece to hold the lower still over a vise etc). If you don't have that stuff, a helper will come in handy once or twice when you need a third hand. But it's not rocket science.