If you're staying in Hackescher Markt, then it would be quicker to take the S-Bahn. At the airport, just head for the S-Bahn station and grab the S9 (S Spandau Bhf) train. That will take you directly to the Hackescher Markt stop (no changes), where you will get off and walk to your hotel - probably on 2-3 minutes. Very easy - takes about 45 minutes, and no changes. You can plot it in Google maps as well, which can show you which way to walk to the hotel once you get off.
You can buy a ticket at the airport (you will have to use the higher cost zone (B-C) or you can download the app ahead of time and purchase it there. Just go to the app store and search for BVG app. It's easy to buy tickets using it. You can also download the S-Bahn Berlin app but that's for planning only. Tickets are purchased on the BVG.