I'm no insurance expert, but have been through a few claims. I've typically faced two possibilities. I can send the car to the shop the insurance will pay for and cross my fingers that it's done right. Or collect several estimates for the repairs and get a decent estimate of the actual car value (recent valid sales on eBay or through classic auto dealers) - then get a check from the insurance company and handle it yourself.
Route 1 can suck because nothing is settled until the car is done, and "done" is relative to the shops involved. Route 2 can suck because if you take a check and find more damage, you're not getting a second check... So make sure any estimate is very thorough. Pay for the estimate(s) if possible to ensure they're proper thorough.
Just my $.02.