I strongly recommend this firm.I traveled with them on last thursday and everything was as they promised.
If you're arriving at Budapest Ferihegy Airport Terminal 1, you can now hop on a train at the airport and travel to the main downtown railway station - Nyugati (West) Station.
It costs 300 Forints (about 80p) and takes about 25 minutes. Far cheaper than other options and faster than most, expensive taxis aside.
Most of the budget airlines fly to Terminal 1. If you're flying BA or another "normal" airline, you'll arrive at Terminal 2 and this tip does not apply to you.
Terminal 1
Buy your ticket back to Fiumicino in the main ground-floor part of the station BEFORE going down to Platform 29. There you will be told that you have to pay 11 Euros rather than 9.50.
Termini Station
If there more than 3 of you and luggage, 1 taxi is not enough. 2 costs $100 dollars each way. Limos? $111 dollars including tip and they were there even when we were 4 hours late! Outstanding
Internet trawl; book in advance, cost deducted the day you travel