sensors that you leave out for a while and then send to a laboratory for them to analyze the radon contents.
Their is a resion for that and it is that radon is not a strong emitter so the photographic emulsion in these types of sensors accumulate strikes over a month or two.
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?
Correct, in fact you would probably not get any radon detected at all as the alpha radiation can't get into the metal or glass wall of a Geiger counter. The only chance would be with a mica fronted Geiger counter but that mainly lets through beta radiation.
See:- Radon - Wikipedia