Where to begin? What to choose from? How to choose?
There are literally hundreds of dances (Wikipedia), but I’m going to assume you’ll be dancing with a partner or a group as a social activity. This reduces your choices to about two dozen choices in a few categories that you have a reasonable chance of finding around where you live. You can find examples of most of the dances listed on the right sidebar, by searching for them on YouTube or by visiting other dance sites on the Internet.
The samples you find will vary considerably in appearance for several reasons. There are numerous styles of many of the dances listed. Most of the ballroom and latin dances exist in two styles namely International and North American, some are danced in a Country Western style. There are line dance versions of many of the dances as well which may be of interest to you if you have no regular partner.
The examples you see may be demonstrated by professionals and amateurs of differing capabilities. The basic elements of a dance maybe so stylized as to be barely recognizable in demonstrations by professionals and championship level amateurs. Considerable time and enormous effort is required to attain such high performance levels. Searches on YouTube yield an abundance of ballroom dance videos. There are many that are represented as instructional most of which are marginal and there are quite a few showing top level competitive dancers but there are remarkably few showing a typical social dance.
Probably the best indication of what a novice can expect to achieve in a reasonable time is illustrated by previews of instructional videos. Some places to see such examples are The Grand Ballroom Video Dance Lessons and Ballroom Dancers.com. Remember that you are watching instructors not students demonstrating.
Select the dances that interest you the most then look for sources of instruction. You will be more likely to persevere learning a dance that interests you. Here is my suggestion. Find a studio offering group classes and periodic studio practice dances. Pick one of Foxtrot, Waltz, Rumba, Cha Cha, or Swing and enrol. Plan on taking eight lessons then try out a studio dance. Chances are that you will have an opportunity to meet other students at various levels and it is even likely that other students will offer to dance with you, yes, both of you. The women in our studio are quite as comfortable dancing with novice males as the men are dancing with novice females. Even if you are asked to dance something you have not learned, accept with: “I’ve not learned that but if you help I’ll be glad to try.” You might find a dance that really interests you.