There are AP Calculus and AP Statistics concerning the most 'mathmatical' subjects that College board offers right now for AP exams. Although taking the AP Stat is very helpful and beneficial for those who later decide to go in to finance, math, research or many other fields but AP Calculus seems to be the most widely taken, most known and most required exam. There is the AP Calculus AB and then the BC exam but you may not take both in the same year. Although BC exam is more difficult and requires deeper and wider knowledge in some areas, it is statistically easier to get a better grade since the grade boundary is a lot lower. AP Calculus is required in many college courses so it might be more widely applicable for your further studies.
I think the most common AP math class is Calculus. Calculus is also the most common required class in college. It can also sometimes be hard to get into. Everyone needs to take it, so it is often full. Therefore getting it out of the way in high school is very useful.
Taught question to answer in general. The info I have comes my public school. To receive an Advanced Academic Diploma with Honors Endorsement, you have to have a "C"or above in Pre-calculus and take 2 honors or AP classes.
As to which AP classes to choose, it will depend on the school you want to apply to and the degree you want. If you are good at Math go for the AP calculus BC, that will look excellent on a college application. But a word of warning if math is not one of your strongest subject, don't shoot so high, at the end of the day a low GPA is a low GPA.
Your AP classes don't have to be in math, AP Biology or AP language are not bad alternative. Many school are looking for a well rounded student, couple of foreign language classes and community service hours are an excellent addition to a CV.
Depends on what school your applying to and your career. If you are going to be a market risk analyst, you might end up taking all three AP math classes!