http://bkv.hu/en/metro_schedules
The Árpád Bridge stop is on the M3 line, the Örs Vezér tere stop is on the M2(where you can find the HÉV to Gödöllő/Mogyoród stop).
You can change lines on the Deák Ferenc Tér stop, where all 3 lines merged.
You will find a ticket at the gates, but if they are out of ticket, sombebody will sell his own tickets at the gates, I’m sure :)