type of diving to do? "a lot" of diving. The main thing that will help you when you actually start cave diving is good bouancy and other basic skills. A lot of folks start their cavern training about the exact same time they start diving in a drysuit and diving doubles for the first time. It would help a lot to already be comfy in a drysuit and doubles before you get into the overhead.
It would also be helpful to have your configuration comfortable, and so I would recommend reading "Doing it Right, the Fundamentals of Better Diving" by Jarrod Jablonski, to start getting your configuration in shape.
I did have my configuration comfortable, and I was used to small doubles, but I didn't get comfy with my drysuit til I started cavern. This meant that I had to get used to the new skills, like reel running, handling my light, etc, while struggling to keep off the ceiling and floor! This is a double handicap. So, I spent a lot of time in the rockpit in the winter with my drysuit. Took about 20 dives to get OK with that, cause I wanted to eliminate that source of stress quickly, and not in a cavern, Thank you.
So, get your configuration appropriate, get your drysuit if you don't already have it, and get at least a small set of doubles to start getting used to. I recommend finding an old set of 72's like the ones I sold yesterday for $150. Not appropriate for overheads because they didn't have an isolation manifold, but good enough for quarry practice. Plus I made $50 on the deal, cause I bought them 2 years ago for $100.
Also, start exercising regularly, like riding an exercycle everyday like I do, (well, almost every day), so fitness isn't an issue as much.