I think "Biturbo" was a nickname that was subsequently officially adopted by Maserati. It simply refers to Maseratis with twin turbos. I believe the first was the 228, which in easily understable Maserati-terms means 2-doors, 2.8 litre. The car I had:
Was a 424v. which means 4-doors, 24 valve - whereas the first where 12 valve. So a Biturbo can be both 2 and 4-doors. As AzzurriGTV says, the 80's Biturbos are really cheap, mainly because the mechanicals are very delicate and need constant maintenance. So you may be able to buy it, but probably not to run it. Furthermore, a lot of them have been abused, so its hard to find a clean, cared-for example.
My 424v was a 1994 car, made after FIAT took over. FIAT introduced a lot in terms of quality control, so these later cars are a lot better than the earlier ones. My car had full service history and was totally original, meaning the previous owner hadnt been tempted into increasing the turboboost, which is an easy wasy of getting more BHP (and ruining the engine). In the year I had it, I had NO problems whatsoever - so I can definitely recommend it.
The Quattroporte is supposed to be even more reliable than the earlier cars, so if you can afford it, I think it would make a great everyday car. Still you have to be aware that although reliable, they still need more - and more expensive maintenance than your regular 164.