As others have said, there are a range of options, from low-cost or sometimes free group classes at community colleges, YMCAs, etc. all the way up to private lessons with national champion dancers. I would recommend getting the best teaching you can afford. In any case, shop around a bit--the quality of instruction varies at all levels.
If you are looking for a dance studio, try the Dance Directory on this site and accessdance.com. Most studios offer an introductory special where you can get a private lesson or two, a group class, and usually a practice party for a reasonable price. If I were looking for a new studio, I'd take the intro package at a couple of them to see where I felt most comfortable.
As far as which dances to start with, you might find a class that gives you an introduction to a few dances. If you take private lessons, your instructor will have ideas about which dances are best for beginners. If you're picking group classes yourself, I'd start with waltz, rumba, and east coast swing.
Happy dancing!