We originally planned to build this using conventional building methods: 2x4s, insulation, and plywood. However, after talking someone that had experience not only building a tiny home, but building a tiny home using a different method - SIP construction. It was definitely a more expensive way to go, but the payoffs seem worth it. First of all, because there are no 2x4s or studs, there are no breaks in insulation which means it should stay cooler in the summer and warmer in the winter. Also, because SIPs are so rigid because of their construction, the structure as a whole should be more stable on the trailer, especially when driving. One of the best things about this method is how fast they can be assembled. Because I had a 3D model of what we wanted, our panels will come precut and labelled so putting them up should be akin to a giant 3D puzzle.
Here's a quick video about construction using SIPs (structural insulated panels)