Car door dented, other party left a note and phone number — how to proceed without losing out?

A bit luckier than last time: today after work I found a big dent in my car door. Under the windshield wiper was a note. The other party admitted that he hit it by opening his door (probably hit and run, then his conscience got the better of him and he came back). He left his name and phone number, saying he's willing to pay. Here's the question: should I settle privately with him for cash, or get his insurance info and go through insurance? If settling privately, where do I get an appraisal, and how much is reasonable? What if he goes back on his word? This is my first time encountering a 'conscientious hit-and-run driver,' and now I don't know the procedure. Please advise.