Definitely strip the car before abrasive blasting or you'll be finding grit for years to come. I am not sold on chemical dipping after having two cars done. Even with the phosphate coating they apply, the car is very susceptible to flash rust, the acid can get caught in crevices and work it's way out later (bubbling your paint) and worst of all, you'll have many closed cavities that are no longer protected because you can't get any paint inside.
Blasting of any type won't remove filler, tar or other very flexible substrates. It's best to remove these by other means to avoid damaging the part by blasting it too much.
More important than the type of media, find someone with experinece in abrasive stripping of body sheet metal and let them use what they are familiar with. Be prepared to get the car primered with a good epoxy primer immediately following the stripping process.
You can see pictures of my restoration on my website below.
