Ditto what MTV, Cary, and others have said about the instructor being more important than the airplane.
Something to feel out that has not been discussed is how supply and demand has changed the tailwheel world. Consider ownership in the tailwheel airplane. How pretty is it. Does the owner/instructor consider it a trophy or a tool. That will have a lot to do with how much latitude you are given to learn. We learn best by doing. I was a loose as a goose instructor who felt the mission was to teach flying, not protect the aircraft. We used to say, "The Army has lots of helicopters." That doesn't always fly in the civilian world. In the civilian world, I flew junk.
My advice is to fly with the oldest, loosest guy you can find in the oldest, junkiest airplane you can find. It will be a tense situation trying to learn in a trophy with a tense instructor. Other than that, a J-3 is a great airplane to learn in. My Dad let me use our D-2 dozer to build a pond for a farmer in trade for six hours in his J-3 when I was nine. Later I soloed in a 90 hp Super Cub at JeffCo. Neither airplane were very expensive at that time and fabric work was cheap. Different world.

