Don't freeze the body, if you can help it(I did with mine). This causes the cells to crystallize & rupture, thus screwing up tissues that may be essential in diagnosing. If you can get it to the vet within a few days, wrap it up and put it in a ziplock bag in the fridge(also, mark the bag 'DO NOT OPEN' or you may have angry family members - trust me, lol).
The one I had done, my vet did not charge for the actual necropsy. I had to pay for some tissue tests that were sent off to a lab, but she gave me the option of doing them or not. That was only around $50 CDN. Tissue tests may or may not be helpful(in my case they weren't really). The necropsy, however, was very helpful and I am really glad she offered to do it.