First off, sorry. That sucks. Just because you can pay it if under $500 does not mean you should. I know accidents happen and I have had the wind take my door a time or two, but if you damage someone else's property, you take responsibility in my opinion. There is no way someone smacked your door that hard and did not notice. They looked and decided they thought they could get away with it and have 0 respect for you. If I know who it was and they ran off, I'd track them down and present them with the bill, evidence, and an understanding that any arguments can be made to the police. If they left a note and stayed by to explain, I'd let them off most likely. But that is just my opinion and we have an issue with hit and runs in my area including some kids who were hit which pisses me off.
For the repair. 100% on the PDR as suggested above. After you get the dent out you can have the paint touched up most likely. A good person can do it so you would not notice it after. I'm guessing prices have gone up, but I'd expect a few hundred for a good job. I don't think you should need to repaint the whole panel.