Budapest airport to Deak Ter

The Metro does not go to the airport. You have to take the bus from the airport to the end of its line, which is the southern end of the blue Metro, which you take for about 9 stops to Deak. Maybe 45-50 minutes total.

At the airport there is a transit booth where you can buy passes. There is a double-ticket available which allows you to make the transfer, costs less than two single tickets. Make sure to validate at each entrance, and retain your ticket until you are off transit, these may be checked for, especially leaving the Metro. You can also buy packs of 10 tickets, which are at a discount.

Taxis aren't horribly expensive in Budapest, I think I'd spring for a taxi rather than hassle with both a bus and a metro with luggage.

Pick up your luggage if any, then follow the black line on the floor about 150 feet to the Fotaxi kiosk outside the arrivals hall. Tell the person in the kiosk where you are staying, they give you a receipt, you take that to the young lady (usually) that assists you in the proper car and makes sure the driver has the correct information. In 30 minutes (depending on traffic) you are at your location for about 8,000 forints including tip. Public transport will cost about 700 forints and take closer to an hour. You could also use the mini bus for about 2000 forints; again figure an hour unless you are the first stop. More here http://www.bud.hu/english/passengers/access_and_parking

I guess that covers all the bases; thanks for the information.