You might want to also consider having a Y-DNA test through FTDNA. They have by far the largest database so you would have the best chance of finding a match on your father line. They are also having a good sale this month. Join a Surname data project for your last name and they can help you understand and evaluate your matches. Generally 37 markers is considered the lowest number for accurate matching.
Y-DNA ONLY tests your father line, your father, his father and so forth, no grandmothers. But it could possibly find your ancestors beyond your 2nd great grandfather. Plus FTDNA provides chromosome matching information so you know you have real matches.
[And I had to trace a 3rd cousin to find a living paternal cousin to test on my father line to test my Y-DNA. Don't stress over what you don't have - close relatives to also test - work with what you do have]