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.