OK, so “I’m comfortable doing that” is right, but *”I’m comfortable to do that” is wrong. Conversely, “I’m ready to do that” is right, but *”I’m ready doing that” is wrong.
Then, “It started raining” and “It started to rain” are both right, while “We stopped to talk” and “We stopped talking” are both right but mean different things.
The various ESL sites I’ve looked at give lots of examples but say there is no rule for these things.
But how can there not be a rule—that is, an underlying linguistic rule (or interacting rules)? Without a rule, how do I (a native speaker) produce the right one every time? And how did all the non-native speakers who do it right manage to learn? Someone—linguists, ESL teachers, successful ESL learners—must know what’s going on here, but I’m stumped.