Seeing as how you were rear ended and more than likely not at fault in this accident. I would definitely recommend taking it to Ford dealerships that have body shops. They tend to give higher estimates than local body shops. As others have said, never let their appraiser near your car until you have had estimates on it.
As for the damage, as long as it was superficial I see no wrong in you doing the work yourself as most of it is pretty much straight forward and easy to follow. But I would at least make sure there was no structural damage before going forward with that plan.