I agree that if the furniture is in fair shape you may want to save it and sand it and refinish it. But if you are talking about a old front porch ladder back chair with 20 years of water stains...then paint is the way to go. I would rough sand the piece with 100 grit sandpaper to get the surface ready, then finish sand it with 120 or 180 grit. Apply a good primer water based. Then finish with a good acrylic latex. If you are going to use the piece out doors then be sure you use a exterior paint. If its a indoor piece then use a interior latex. Remember the pride is in the preparation, a million dollar paint job will look cheap if you did not take the time to sand and prime. Good luck with you project.
if its antique you shouldn't touch it. if you care about the value tanking. if its not valuable or you really want to paint it, if it has a vanish on it, you need to buy whats called stain killer and you use it like your painting it on, then you paint over it and the paint will stay. latex or oil based.