Your first decision is whether you want to learn in sidemount or backmount. If you want to learn in sidemount, there is no better way than by going up to Cave Adventurers and taking sidemount/cavern/intro with Michal or Edd. I do not recommend taking cavern separately as it is extremely limiting and you'll be back very soon for intro. Cave Adventurers is one of the only places where you only have to show up with mask/fins/exposure protection and you can try all of the different gear they have before committing. This is very important in sidemount because all of the rigs are very personal to the diver. Backmount is pretty universal so you don't have to worry about that.
If you want to learn in backmount, then I'd stay in the Ginnie/Peacock area and take it with one of the instructors down there. If you believe in what GUE teaches and want to stay in backmount, then go thru a GUE instructor and take fundies. It's a good course anyway if you want to stay in backmount, but will make you a much better diver.
With cave diving you need to start at the end and work your way back to find your path, then you need to take an honest look at where you are and evaluate what you really need to get there. Cavern/Intro is often described as the hardest course people have taken because they weren't good divers to begin with. They may have thought they were, but they were sadly mistaken. Cave courses are not meant to teach you how to be good divers and the entrances to the caves wear many battle scars because of this. If you want to do sidemount cave, there is literally no reason to start in backmount, whether that sidemount is due to the side of the passages, or any of the other reasons to choose sidemount. If you have only taken OW/AOW from a PADI shop and don't look like any of the number of GUE or real cave videos on Youtube, then you really should take an intro to tech type course, find a mentor, and get your diving skills down first. A cave is not the environment you want to learn how to kick, backup, and control your buoyancy in. For the health of you, and more importantly the long term health of the cave.
