Well the model is split up (as in, the head, body, arms, feet, and hands are all separated from one another) so the order you build it in is entirely arbitrary. I personally built the cap, body, feet, head, and then the hands but it doesn't matter what you build first; just keep in mind that you should build everything first before attaching them to each other, otherwise you risk not getting the pose right.
While some use lighter paper, I use cardstock because I like to be able to pick up my models. I think the lighter stuff is just too fragile, although it removes a lot of the shadow that results from cardstock's thickness.
It would be impossible for me to explain all the "rules" I've developed through making so many papercrafts or the type of improvisation and intuition required to make this kind of craft. Again, the best way to learn is through practice.