here's my take on it, so take it with a grain of salt.
Take full cave first. You can do a whole lot in caves being able to make a single jump, or do a traverse, and not rack up deco. I.e. you can spend a year and a half in Peacock without racking up deco if you have the ability to make a traverse or a couple of jumps. Heck, the Grand Traverse does not have mandatory deco if your surface intervals are long enough on the way. I would personally do that sooner rather than later if you trust yourselves to limit your dives to your comfort level. I hate being restricted by not having the training or the c-card, I want to be restricted because I don't have the balls to do that dive yet.
Once you have found that you are surpassed the limits of full cave, PSAI has a great new course out called something like Cave Staged Decompression or something where you learn stage diving techniques and it incorporates AN/DP into that class. Gives you more range in deeper caves like JB or LR when you really need to have the accelerated decompression. Great combined course option that I would like to see brought into other agencies.
Being able to do decompression when you are limited to linear penetrations on 6ths isn't going to do anything for you, however being able to make navigational decisions while diving to thirds is going to open up a lot more caves for you. Only when you have exceeded the limits of full cave, should you find the need to get decompression. NOW, that being said, I am biased in my direction because I was trained in the Peacock area and there are a lot of shallow ish passages and the caves have depth profiles that has you basically doing decompression while on your way out the peanut tunnel, so decompression can be avoided by strategically planning your dive so that while you will obviously exceed NDL's, by the time you get back into the cavern zone, you have no decompression obligation. If you dive primarily in caves up in Marianna, or Ginnie, then you should probably have AN/DP incorporated into your full cave course because caves like Jackson Blue, Little River, and Ginnie are very limiting on penetration due to the chimneys suddenly dropping you down to depth.