Before you strip it wipe the table down with mineral spirits. I can't tell from the picture if the stain has been sanded into on that spot. If the color is uniform you might be able to recoat the table instead of completely stripping it. When you strip a table it takes out the grain filler with the finish. The surfaces scratches as well as a spot that has been sanded with melt away if you would recoat it with lacquer. The color of the table wet with mineral spirits would give you an idea of what it would look like recoated with the exception of the white around where you have been sanding on it. It would take lacquer thinner to melt the white away but if you use lacquer thinner spray it. Rubbing it would take the finish off.
If you choose to refinish it I would glue any loose veneer down first and then strip it with a methylene chloride stripper, soon, it's getting close to winter and strippers don't do well below 70 degrees. After stripping sand the table top starting with 180 grit paper and finish with 220 grit. Then use a grain filler. The oil based mahogany grain filler that Mohawk Finishing Products sells is about the perfect color to stain the table. It is usually all that is needed. Fill the grain according to the directions and let dry overnight. Then sand the residue off with 220 grit sandpaper and finish. The old finish on the table is a nitrocellulose lacquer but there is no reason you can't use any finish. If you have the means of spraying I would probably seal the table with a vinyl sealer and topcoat with a pre-catalyzed lacquer. A table top like that almost has to be sprayed regardless of the finish you use. You could do it by hand but the hand rubbing labor would drive you nuts.
