As a 65-year old newbie OW diver (certified in 2008, never dove, now starting up again) I have no advise regarding the technical path you might take. My question is your motive for your end goal - why do you want to be a certified kick-ass cave diver in 2-3 years? Your motivation for the goal is going to bias everything you do along the path to enlightenment.
Do you want to dive caves purely for recreation - diving in caves already mapped and available to explore? Are you wanting to push the boundaries and explore new passages? Do you want to join a team that is linking systems in Florida, Mexico, etc? Perhaps you're of a scientific bent and are interested in aquatic speleology. Just to become a "cave diver" is sort of a vague goal. You'll retain your motivation to navigate the complex chain of instruction and experience outlined by others if your goal is more concrete - "I want to dive Sump 7 at Sistema Huautla."
Although I'm a newbie diver, I have accomplished a few other things so far in my life. I'm an experienced alpine mountaineer, achieved a paraglider pilot license, and was a high level ski instructor for many years. None of those achievements were done for just for the sake of having another notch in my belt. They all came from a love of nature and the natural environment.
If you look deep into your motivations for this cave quest - you just might find an interesting and thrilling career path. My interest in mountaineering drove me to college degrees in geology - and at retirement age I'm still in love with my profession as a geologist. Maybe a bit of introspection in this area will help you resolve questions more important than "do I need AOW or not", but would a degree in marine biology or geomorphology or entymology or archeaology or maybe even geology springboard your love of diving into something really interesting? Just think, pursuing the right Ph.D. might get you free training with NOAA or USGS, maybe even NASA. At 18, the possibilities are nearly limitless. My simple advice - don't lock your thinking in on something as limited as a certificate with your name on in.