Get all the parts you can off the car. Give them the doors, hood, deck lid, valence panels all separately. Make sure the are using plastic media or soda powder and NOT SAND. Sand will definitely pit and warp body panels. Like was already said, thick tar or under coating will not come off easily with media blasting and they generally won't take any effort to get that stuff off for you. To do a complete car, expect around $1200. Also, don't expect to get your car back in a week. The place that did mine also does a lot of comercial work like truck trailers, large tanks, etc... and they did everything on a first come first serve basis. In my case, I got the car back in about three weeks. Like hotrod98 said, get it primed immediately. Some places will also do that for you. The place that blast my car offered it for $600. I, personally thought that was high, so I did it myself.
Here is the website for the place in KC. There is some good info on there to better understand some of the options.
http://www.eagleautostripping.com/