Do I really need to strip the paint all the way down to the sheet metal? Or should I just strip the finish and primer over that? What would be the advantages if I stripped it all the way down to the sheet metal?
It depends on the finish that you have on your car. When I painted my exploder i sanded it but left the paint on the car and did my body work over it. On my mustang I blasted the whole car to remove all of the rust that was hidden under the paint. I mostly wanted to start with a clean slate and now I know what is under all the paint.
If it's a new car with the original paint it's fine to scuff it and shoot it but when you're dealing with old iron you don't know what's under there, how many paint jobs, damage, etc. Ideally strip it to bare so you know what you're dealing with, it's a pain but worth it. Your paint job is only as good as it's weakest link so you're taking a chance going over the old work.