No expert on this, but some beta emitters are counted by using a chemical that scintillates (flashes) when a beta particle hits it. Going back a way when working with sulphur 35, I used a chemical with a long name abbreviated to POPOP. The method is called liquid scintillation counting
The downside is that you needed pre-nuclear testing steel and lead shielding to put the photomultiplier in.
For anyone interested in useless facts, a large source of uncontaminated materials was heavy steel plate used in WW1 battleships sunk in Scarpa Flow.
Radon in seawater is measured by freezing out the radon with liquid nitrogen then using a Geiger counter.
The problem with Radon is that it is chemically inert like all the noble gases (neon etc.) so chemical methods don't work.
If it's health critcial, I would be looking at a commercial unit.
No, it's not health critical, and to be honest, I don't really know what to look for. I mean, Im starting to realize that Radon itself, being an inert gas, like you said, is hard to measure directly. I guess all I can do is just measure normal radiation (not sure if alpha, beta, or gamma), so I should be able to use a normal geiger detector. But in this case I would be getting levels derived from other sources, not only Radon, right?