I am going to add a bit to ally's excellent answer.

Suggestions
Start with a 37 marker Y-DNA test from FamilyTreeDNA. Theirs is the largest database and most accurate test. This tests the father line only (your father, his father, his father...) but can accurately predict a father line. It doesn't promise results unless your distant cousins have tested as well, and it may take time before they do, but it will give you the most accurate results once they have tested.

If you took the 23andMe test before Dec 2013, the results can be transferred to FTDNA. It is well worth the money. I can't recommend AncestryDNA at this time because the questionable trees and lack of any chromosome matching tools can lead you down some very wrong paths.

In a few weeks, when GedMatch is back up and running, do upload your 23andMe results there.