I don't know if I am qualified to answer...just experience...
First, what country are you from? It will determine whether or not you will want to learn Latin, Standard, Smooth or Rhythm.
American Style=Rhythm and Smooth
International=Latin and Standard
The differences in American and International are numerous but for a beginner boil it down to American allows seperation of the partners and is slightly less technical. The dances aren't all the same, for example you only see a Quickstep in Standard.
Most people learn a grouping of either all five of the latin/rhythm or standard/smooth, or they learn all ten within the group.
You can lose your versatility and get confused and set in your ways if you don't learn more then one. Also, the steps often overlap from one dance to the other but the rhythm foot and body positioning changes the appearance, you don't want to create a kinesthetic block that allows you to perform a step in only one way. You are running that risk if you just learn one dance.
HOWEVER, if you are determined to learn only one then...Foxtrot or Rumba.
They are considered in their seperate categories to be the most important to master as they each require a technical proficiency that can and does often cascade into your other dancing, improving everything.
If you can, learn many dances and start with the most basic steps. In a few lessons you should be able to have an understanding of the basics of multiple dances and that will mean you can go to social events and practice.