Additional option: most of the tickets (including the Airport-City-Day Ticket) can be bought in the MVV phone app. If you have roaming data or use the airport WiFi, this can save time and eliminate the need to worry about lines for the ticket machines, chip & PIN support for your credit cards, etc. The interface for most tasks appears in English and other languages, though a few screens are only in German.

I generally buy my ticket into town while I'm waiting for my bag, then walk straight to the S-Bahn platform.