Wow,
Some interesting info here.
Generally, I find a few models quite popular in the caves here in Florida.
Sidewinder reels by either Salvo, Halcyon, or Dive Rite. The Salvo and Halcyon reels are quite similar with only minor differences. Personally, I have the Salvo but either works well for me. The Dive Rite Sidewinder reels are ok, but generally made out of weak plastic and it WILL break, unlike the Delrin of the Salvo and Halcyon reels. Larry Green has been selling a newer sidehandle reel that is very tough, but I dislike the metal handle. They are smooooth though. Really nice.
Top handle reels are popular with a lot of the old school guys. You'll find these handles on some Dive Rite models, some Ralph Hood models, Larry Green (rebrand of the Ralph Hood), and some others. I tend not to like these as much because they are the devil when trying to manage the light and the reel with the same hand. They are still popular though, and people do like them. I used them for cave class, and then went and bought a side handle!
You will also see some reels with mechanical features. Clutches, cams, all kinds of things. These are rarely seen in the caves, but seem quite popular with wreck divers from the northeast. Honestly, with a stone ceiling over my head, the LAST thing I want to worry about is my lifeline home getting hosed up because of some mechanical device. This is one place where the KISS principle can get you out alive.
Keep the length reasonably short. About 400ft of line is PLENTY. Closer to 350 would be idea for a cavern. Make sure it comes with #24 line on it. Not #18. And some of the wreck reels come with the heavier #36 line. That's ok too, you'll just get less length on the reel.
Not sure what Joel meant by not using a light since you'd be in the light zone. Cave agencies teach that you need a primary and 1 backup in cavern zone. The third light is the sun. In cave, since you are out of the sun's reach, you each carry a third light. You WILL be using your reel in conjunction with a light in a standard cavern course, so I suggest you keep that in mind. His advice to get a sidehandle model is probably right on the money.
Best of luck.