Car rental is easy in Budapest, Hungary.
A selection of larger car rental companies:

• Americana
• Avis
• Budget
• Hertz

In general, all car rental companies require that the person renting a vehicle is at least 21 years old, has had at least driving experience of one year, has a valid driving license and passport.
All the major rent a car companies have an office at Ferihegy International Airport Budapest. Brochures on rent a car options are available from hotel reception desks and Tourinform offices.

There are minor car rental companies as well like Steverent. Or you can hire limousine airport transfer from Limo Hungary.