Good old paint stripper, applied with a wide art brush, sections at a time, worked for me.
Takes the frame down to primer first, then a second application will take it back to bare metal. Usually, you will find very little in the way of grinding or sanding was used on the original frame. The remover means you don't have to work into little nooks and crannies around lugs and the bottom bracket. Wash off with suitable thinners, such as acetone.
If you use a wire brush or sandpaper, you might get scuff marks that will appear through to the final finish, unless the powder coat is thick enough, or you apply several layers of primer and finish back with 1200 or 2400 wet (as in water and dishwashing detergent wet) wet-and-dry paper.
The process, of course, requires patience.
I'd consider applying several coats of clear finish irrespective of whether you go the powdercoat or spray paint route. It adds a degree of durability, I've found, including a little bit more resistance against chipping, and helps maintain the gloss.
The last frame I painted was with a couple of cheap cans of spray enamel over several coats of reasonable quality metal primer, then topped at the end with several coats of clear. Worked well on the MTB considering the lack of care shown by the person I lent it to for 12 months.