Lots of good information in this thread for you to keep in mind in the future if something ever happens again, but I'll just throw in my
1. In Texas it is legal to record a conversation if you are a party involved in the conversation - only one party must agree, you do not need permission from the other party(s). I have this first and foremost in my mind if I get in an accident. Look up the laws for your state - only about 12 have more restrictive requirements for conversation taping. If I don't want them to know I'm recording them, I will just put the iPhone on video record and act like I'm taking individual photos and then just kind of hold the phone in my hand so it can continue to pick up the conversation. Do not let them move the car until you have full evidence via video or photo - if they refuse to let you document the accident and try to move their car, you now have record of them doing so and a good arguing point for later.
2. I generally call up the insurance company on the spot. My wife got in an accident near our home and I just happened to be on my way home and really close. When I got there, the douche that hit her admitted fault to me but also admitted he did not have insurance citing some dumb excuse why not. I immediately called Nationwide and got them to take his statement over the phone right quick (I just called and said before I give you all the accident details, please take this gentleman's statement who just hit me). Sure enough, Nationwide called me later that night and said he was trying to claim now that it was my wife's fault. They told me not to worry because they already had his recorded statement.
I've been lucky enough to have police officers as witness to several accidents where I've been hit. Every single one tried to claim it wasn't their fault when I'm standing right next to the officer who has already told me they saw everything and will stand by me. One lady didn't speak English, no driver's license, no insurance, plowed into me at 35 mph while I was trying to turn into a driveway. A cop in the parking lot I was turning into saw the whole thing, and said she didn't even look like she tried to slow down. Her story was that I had cut her off... except that I was in the right lane about half a mile back. People are f***ing ridiculous.
Also, I recommend uninsured motorist coverage if you feel the need. Living in Texas, I feel the need. In addition to that, if your car gets hit while parked or is involved in a hit and run, they can claim it under uninsured motorist and you don't have to pay deductible.