You are absolutely on the right track. I highly recommend you go to www.familytreedna.com and search on the DICKASON surname project. You get a price discount when you order a test through the surname project. My surname is BARTLETT and I have done Y-DNA with that project. However, #29244 in the DICKASON project is from my line, so I hope your test matches his, and we would all be cousins.
It is good to start with the Y-DNA project. Someday, you may want to take the Family Finder DNA test. I've had that one and we may well match from that test. You can read about the FF test under the FAQ tab on the FTDNA website. And feel free to ask me questions anytime.