It's a real case of doing your homework, which you are doing now!!
You sound as though you want whatever you do to work for real, so with that in mind remember that there are big differences between different styles for example Karate is very, very varied, from fullcontact to semi contact, sport to traditional.
One thing is you need to find something that is close enough to go to, so do as Sharon says, make a list of clubs that you can get to easily then visit them!
Also, get your mom or dad or any adult to ask questions. Remember there are a lot of Martial Arts schools just trying to make money - that might not be for you, especially if you are on a budget.
Can anyone think of questions that should be asked?
* What is the liniage of the School?
* Are you affiliated to a governing body?
* Do you participate in competions of not?
* How much will training/ suits/ equipments/ gradings/ licence/ insurance cost?
* Do you have seperate classes for young people?