I just noticed that you posted this before,
@brewmeist.
There is
typically no reason to check headspace a barrel on an AR-15. I say this, because when we're talking about "Mil-Spec" (which is another name for "loosey goosey") there is already a little play in the chamber, so the rifle will reliably digest just about any round by any manufacturer. If you bought a standard 5.56 barrel, then
typically you are good to go after getting 40 lb-ft of torque on the barrel nut and putting everything else together correctly.
I used "typically" in italics there twice, because when I assemble uppers for customers, I always check the headspace with a field gauge and an no-go gauge. The U.S. Army will allow a rifle in service if the bolt closes and locks up on a field gauge, whereas the Marine Corps will only allow a measurement with a go gauge. If you end up with a short chamber (which I have very infrequently) you need to use a chamber reamer and adjust everything little by little to get everything right. If you end up with a long chamber (which I have never found in 40 years) there is a lot more work involved on a lathe to take some of the barrel face off. At that point, it would be cheaper to get a new barrel.
One way to make sure that you have a "plug-and-play" head space fit, is to buy the barrel and bolt matched together. Some "high-end" .223 Wilde and competition barrels are marketed this way, but they are typically kind of pricey. More so than a $50 headspace gauge.