This is always a bit of a tricky question. My buddy (dead a few years now) ran a stripping shop for decades so I have a little experience.
Whether veneer or solid wood. I would start out with stripping first for various reasons. Gets the top layers of finish off, pulls some of the finish out of the grain, reduces overall sanding amount and therefore loss of wood thickness. After that you can move onto finer sanding.
Doing a whole set is a lot of work. I don't know that I would tackle that either from a time perspective or breathing that crap. If you don't have a dedicated garage/patio space you can keep the pieces while working on them I would lean towards not doing it yourself. I personally wouldn't do it in my shop. The amount of time it would take would make my shop smell like stripper for far too long and make doing anything else in there miserable.
If you decide to take it to a shop and don't have a place yet. Go check them out, see some pieces they are working on, make sure they know to use various grits of steel wool, no wire brush on veneers, if Oak keep the water to a minimum, (hot water bathing with steel wool and stripper is a common technique) etc.
Good luck