House boat cat hull plans

The simple flat bottom barge shape, with proper slope bow and stern, will suit your purposes better than a cat in terms of stability, storage, and much lower cost.
The cat's only advantage is efficiency of propulsion, at the expense of much much lower displacement capability, I would guess the picture you originally posted would only allow about 10% of what a flat bottom barge would accommodate.
But propulsion of the flat bottom barge would not be very difficult, as mentioned in previous posts.
As far as hull building, welded steel is the most practical approach, far far less hassle than other construction methods, and easily built for decades of reliable service.

 

You could find an old floating something with a lot of character, fishing boat, barge, tug, whatever (maybe even an old worn out catamaran) and convert it into a houseboat. With or without keeping the original exterior appearance. Plenty of those should be readily available around the Med.