PADI broke up their Tec diving course into three components and the intro class, Tec 40, covers a lot of the skills and theory you will need to use doubles properly. If you are interested in cave diving anyways, as you mention, I would recommend taking the PADI class, if you are PADI oriented. Of course, TDI and other organizations have their equivalent. Pick the organization and more importantly, the instructor that you are most comfortable with. Renting doubles is a good start, but I strongly recommend getting your own equipment before you move too far into the Tec direction. Having a proper fit and being comfortable with your equipment is many times more important when doing Tec diving than recreational singles diving.
-Frank
-Frank