Hi. Firstly, "It got me thinking ABOUT the importance of personal safety" One main difference between the two is that one is planned and the other isn't. Example: The power cut got us thinking about how much we rely on technology nowadays (It wasn't planned, but the fact that we were suddenly unable to use electricity made it a relevant subject). Our university lecturer got us to think about how much we rely on technology nowadays (Intentionally, as part of the lecture).

I would phrase that as "The accident got me thinking about the importance of personal safety." You could also say "The accident got me to think about the importance of personal safety."