score:3
The transfer ticket is basically two single tickets rolled in one, sold cheaper but with the restriction that the second trip must take place within 1Β½ hours.
If you need to take a bus, then the metro, then a tram, that's a total of three tickets, which you can decompose as one transfer ticket (HUF 530) plus one single ticket (HUF 350, or HUF 300 if bought in a booklet of 10).
That's assuming you can purchase a transfer ticket: apparently they aren't sold everywhere. They should be available from the BKK desk at the airport (there's one in each terminal), but if you arrive after the desk close, you'll have to purchase your ticket at a vending machine which might not have transfer tickets. I remember arriving late in the evening at Budapest airport and buying two single tickets to take the bus+metro into the city, but apparently new ticket vending machines are being rolled out, so this might have changed.
No matter which ticket type you get, remember to validate it before each segment of the trip: the tickets never come out of the vending machine stamped. You'll need to validate one ticket at the airport, then one (or the other half of the transfer if you can get one) at the metro transfer point, and another one to get onto the tram.