In jersey it costs 125 per hour to have a car media blasted where they use plastic media or aluminum oxide. Do not have your car sandblasted. Sand will warp your Panels and any sand that stays in the car in cracks and stuff will hold moisture. Not good. Chemical stripping is very expensive if you can find a place in your area that even does this. Just remember chem stripping will take off everything that is not solid metal. it wiil remove all factory sealers paint primers and anything that is plastic. so you will have to remove anything that you dont want gone. If there is any rust it will remove that also. With the media blast it usually cost between 700 to 1000.00 dollars for an average sized car, like your stang. Hope that helps.
Sand wont hurt the car if the blaster knows what they are doing - most professional shops should. Its $60 an hour here for sand, $80 an hour for media.
I will tell you the same thing I tell everybody. Sand CAN warp your panels, so can plastic, walnut shells, soda, manual sanding, etc. That doesn't mean it WILL.
Sandblasting is fine IF you go to somebody that knows what they are doing. I had my car done by a reputable shop here in Cleveland, cost for the shell inside and out, top and bottom was about $450.00. best $$$ I have spent yet. There is nothing like working on clean metal .
Make sure you ask lots of questions, make sure they are familiar with classic cars, DO NOT go to an industrial blaster. Ask to see pictures of cars that they have done in the past. I chose sand over beads because my car and some rust that I wanted GONE. Beads wouldn't have done that for me. Oh yeah sandblasting will find rust that you never knew existed and may have not known about, until you laid down that nice new paint Be ready to do a little more metal replacement when you get the car back than you originally planned.
Be preparred for sand to be in EVERYTHING. Actually any media blasting method will have this problem. It gets in everywhere. You will clean your car out again and again and again and you will never get ALL the stuff out. I highly recommend buying/building a rotisserie. If I didn't use one my car would still have about 25lbs of sand in it that I never would have seen.
I don't have any experience with dipping, I know that it is expensive and hard to find places that will do it (around me anyway). And the same places that trap sand could trap solution. But on a rotisserie the solution would probably be easier to remove than sand or media.
Sandblast 007 is an after pic, and 002 is a before.