If your travel agent booked the transfer you are already paying somewhere in the neighborhood of 30 euro (nearly 10.000 forints) for a 22 euro (7.000 forint) ride, so tip what you want. The driver will also be "tipping" the hotel. If you like him and he did a good job, give him what you feel comfortable with. There is no science here.
What will happen is you get off your plane, pick up your bags and go out the black glass door to the arrivals hall where the driver will be waiting with your name on a sign. You will then be escorted to the curb where he will say, "wait for me i will be back in under 5 minutes". That's because he is not allowed to park except in the general parking lot. He has to go fetch the car.
While you are waiting, please observe the passengers who arrived with you who choose to take a tax. They followed the black line marked "TAXI" on the floor which began in the baggage area. In the time it took to find, meet and greet your driver, they will be at the Fotaxi Kiosk (just feet from where you will be standing). Before your driver reappears they will have been given a ticket with the address on it, the maximum charge on it and the number of the cab they have been assigned to. Show to the driver to confirm you will be taken to the right place. Still before your driver reappears they will be in their cabs heading off to beautiful downtown Budapest. Their charge will be something in the neighborhood of 7.000 forints or 7.500 including tip.
Now, when i have guest going to Budapest that i want to ensure have a great introduction to the city I hire a driver named Laszlo MARKUS ( http://silverwings.hu/ ) for a nice little charge picks them up at the airport (same conditions as any other private driver) but then gives them an orientation tour through the city and along the banks of the Danube. By the time he is done (less than 1.5 hours) you will know where everything in town is, and have an idea of where things are relative to your hotel.