When I first started doing Cerakote I used a Paasche airbrush. It worked pretty good but was prone to clogging a bit. Cerakote flash dries pretty quick and is bad about building up in the gun/brush. Most of my work is done using stencils so a real fine spray pattern is not needed anyways. Later I went to the cheap HLVP gun that Cerakote (NIC Industries) used to sell on their site. It was just about $40, and it has been a great gun for me. I have used it a bunch Cerakoting Yeti cups and such, and really have got my moneys worth out of it. I think this one is the one they ended up replacing the cheaper one I have with. At $55 it still looks to be a pretty good deal to me.https://www.cerakoteguncoatings.com/finishes/SE-273/paasche-hg08-hvlp-spray-gun/
A shop air compressor is fine, with a few caveats. You need a good way of regulating pressure, and you really, really need to get moisture/oil in the line under control. My compressor has the main tank, and I drain moisture pretty often. Then I run the air through a copper coil, kind of like a "worm" on a still, to cool the air and condense moisture out of it. Then it goes to a second tank, and my moisture separator is on the outlet of that. I realize that is kind of extreme. But when you are doing a lot of work for other folks it matters. You can probably get away with just a good moisture separator on the outlet of your compressor. But more is always better and leads to less frustrations.