Yes, plenty of people use the app. It is simple, straightforward, and very easy to use.

BVG @ TXL
 

I buy my tickets/passes at the BVG info booth just inside the terminal. The staff all speak English and they are very helpful.

Some times I'm such a geek. You know what I've done?

I've used the VBB-Livekarte live map to compare getting the TXL to Hbf and then a bus with departing at the same time and changing onto the first S-Bahn and getting the tram.

There's a cigarette paper between them, it's that close!

I think I might just go for Bus S-Bahn-Tram as I'm a bit of a transport geek, and a multi-modal journey would be a bit more fun.

Of course, I'm guessing that whatever I choose to do, if I get any ticket for zones A and B at the airport, I can use any of these modes of transport?

Yes, you can.

Bus, S-Bahn, Tram all valid with A/B tickets.

Thanks,
Is it like in London, can I also use the DB trains within zones A and B as well, such as between Alex and Zoo? Or do those require a different ticket or a supplement?

You may use S-Bahn and regional trains operated by DB. You cannot use long-distance trains without a supplement. E.g., an ICE from Suedkreuz to Hbf (Central Station) is not included.

No, you can't get on an ICE (but between Berlin stations, no one is likely to check).

...which is what I wrote.

Yeah, but your internet is faster. My dial-up modem is really slow these days. ;)

It seems that some of the DB trains (RE/RB) between Charlottenburg and Alexanderplatz are not running next week, but the S-Bahn is still in operation. Also some north-south routes are curtailed/split, for example the Szczecin train seems to be starting from Bernau or even further out, which is annoying for my plans.