Before getting started, it's worth considering that not all hot rod project cars are a good candidate for this style, although it depends a lot on the owner's particular aesthetic preferences. But the car's structural integrity is important no matter what the desired result. A shell that's heavily damaged or caked with body filler isn't a good candidate to bare it all, and, of course, the car's body panels and other bolt-on parts (like door handles, bumpers and even body trim pieces) have to be actual metal. Composites, plastics and cheap aftermarket replacements just won't work. In fact, this is where some of the more talented metalworkers take the opportunity to show off their skills, designing and fabricating custom metal parts for items that need to be repaired or replaced.
After the specimen is chosen, stripping off its paint is just the first step. Sanding is crucial, and there are various approaches. Using tools such as angle grinders or rotary sanders will get the job done efficiently, although perhaps lacking the delicate touch that the most particular of builders prefer. The most finicky sometimes hand-sand the car, which is a long and arduous process, and can be accomplished with sandpaper or other abrasives, including steel wool. It takes a lot of arm and shoulder strength to penetrate and remove the layers of finish on a car, especially a vintage hot rod, which is likely to have had several coats of paint applied over the decades. A combination of approaches, using power tools for large areas and manual sanding for smaller and more intricate areas, is a solid strategy. Another option is to blast the car's shell clean with a media blaster, using the appropriate abrasive for the specific job -- sand, plastic or glass beads, even bits of walnut shells are among the many possible options. This might require transporting the car to a well-equipped body shop or custom-build shop, or you might opt to purchase an affordable kit that can make the job possible right in your own garage (though it will be messy). Chemical strippers are also available. Whatever the approach, it's important to not cut corners with the paint removal. Getting the metal as smooth and as rust-free as possible will make the rest of the process much easier, although it's still just the beginning.
The newly naked car is likely to reveal some flaws that weren't visible under the paint. A skilled metalworker will enjoy the opportunity to show off his or her talents and make everything perfect once again; but others might decide to simply not bother with minor cosmetic repairs. Both avenues are totally acceptable and embraced within hot rod culture -- it's a matter of personal preference. Either way, if metal repairs are going to be made, now is the time to do it.