You ask about "lay-up". Does this mean that you plan to do the lay-up yourself? There are a few BPL members who have experience with composite layups, but you might get more detailed advice on a composites forum. People there could answer specific questions about prepreg tapes, vacuum bagging, etc.
It would be much easier, I think, to use stock carbon tubing for the frame. I think you could find nylon, Delrin, or aluminum joints in many configurations, or you could machine them yourself if you have access to the equipment. If you want flat composite panels, these can be purchased off the shelf from a handful of online suppliers. Sandwich panels with hex accordion spacers in aramid, carbon, or aluminum are available, as well as foam and balsa. They are all fairly expensive.