Both CCR and cave diving are advanced forms of diving, and combining them adds complexity that compounds. Therefore, I recommend gaining significant experience before attempting to combine them. Most of Texas is just a couple of hours' flight from Quintana Roo, where there are ample opportunities to rack up serious hours of cave diving on open circuit due to the shallow caves here. Regardless of where you choose to dive caves, learning on open circuit will build your cave diving skills without unnecessary complexity.
It's a bit harder to argue for doing a lot of deep open circuit trimix dives before transitioning to CCR these days due to cost issues. However, having been there and done that, I still believe it's the "better way" in terms of diver capacity, even if it might not be the most economically sensible choice anymore. When your CCR fails, you instantly become an open circuit diver. Building your open circuit capacity over time will be beneficial, rather than desperately trying to remember the bailout procedures you learned in your CCR class.
So even if you're tempted to jump directly on to the CCR at least doing some extended dives on open circuit would build the right kind of capability