I only recommend a walking tour, if you enjoy walking, do not have any physical limitations, have more time in Budapest (2-3days) and would like to have at least two half day tours or a full day tour. It is wonderful to wander around in a new city, that is just for you to discover, but with a relaxed, not rushed tour it is best spending actually more time at each on the selected sights, rather than just walk for the sake of “walking”. Budapest is quite big, so merely a walking tour would be almost impossible, so a walking tour is a combination of a tour on foot with using some public transportation occasionally (trams, buses, historical underground). You may buy a transit pass, single tickets for the public transportation or the Budapest Card, which provides free public transport, as well as free or discounted entry to museums and other places.
This way you will also learn, how to manage the local transportation system! In case you would not like to use any public transportation, we would concentrate on a specific area or neighborhood of the city only.
The minivan tours are really great ways to explore the city. Between the sights you travel in a comfortable, air-conditioned minivan, which is driven by a professional driver, who only takes care of driving and parking. Since the traffic and especially parking can be quite hectic at times, it is very convenient having the minivan driven by a driver, as this way there is a flexibility of walking shorter distances with your guide and be dropped off and picked up at different locations. I think that driving and guiding at the same time, is not safe! The guide can only concentrate on you and your tour this way! Budapest is a big city and is quite spread (you will probably be surprised by its size, after you arrive!), so in case you have a limited time or you would like to see a lot, I would definitely recommend having the tour/s by minivan. You may see much more and have an orientation of the city during a shorter period of time. Of course a tour by minivan does not mean, that you sit in the van the whole time, actually you do get out several times, walk around, enjoy the views, go inside and visit the different places of interest.