Here's an informative website you might find helpful. It gives a few variations on"readiness" checklists, plus tips on various training strategies, the best ages to start them, and the advantages and disadvantages of each approach: http://www.parentingscience.com/toilet-training-readiness...
I've known lots of young parents who have done exactly what you're doing – followed their children's lead. Sometimes it results in a fully-trained child within a few weeks.
Not uncommonly, a child seems trained for a few weeks, but then completely loses interest for a few weeks or months. This very common outcome has resulted in some pretty sad power struggles – parents are so reluctant to see their child "backslide" that they forget he got as as far as he did because he was choosing freely. I've noticed that in families where the child is allowed to change his mind, it usually doesn't take too long before he decides the benefits of using the potty are more attractive to him, and then training takes for keeps. (You read many such stories on this site.)
My own daughter trained at her own speed, and decided she was trained shortly after age 2.5. Her son did the same, just before he turned 3. No sweat or tears, no rewards or punishment, the children had just heard enough positive messages about the joys of using the potty, and they went for it. I've come to realize that this is a developmental step much like walking or talking – most kids WANT to do it when they are ready.