If you want a test to look for possible genealogical matches have a look at FTDNA's Family Finder test. Any matches will tell you the approximate relationship eg 2nd to 4th cousin.
The minus to this test is that your maternal and paternal "cousins" will be mixed up so you will not know which side of the family they are from, so it may be more difficult to find out where you connect with them.
YDna is for males only so that's out for you, unless you have a brother. This test is to trace the male line and the surname.
MTdna will follow your maternal line, so mother, her mother, her mother and so on. If it is anything like the YDna test, any matches may be so far back in the mists of time before records began, that you would have no chance of finding a connection.
This is my take on the tests available through my very limited experience, and even less knowledge and understanding. I found the Family finder test results interesting though I have not found a cousin match with anyone yet.
