I recently built a back for a camera and can say that the experience was quite an education. There is a learning curve attested to by piles of sawdust on the garage floor. If you're going for a 4x5, I can recommend the advice I've read elsewhere of purchasing an old Graflok back and adapting it to your design.
Based on the sawdust factor mentioned above (but not knowing your level of woodworking expertise), I'd stick to less expensive and readily available woods. If you can make it once, you can make it again with better materials once you get the hang of it. You'll always end up with sawdust. But cheap sawdust is better than expensive sawdust. Having said that, cherry is still a good choice both practically and aesthetically. It is a beautiful wood. It darkens with age and with exposure to UV which somehow seems appropriate for use in a camera.
Also, as Jay suggested, laminates are a possibility. However my knowledge of laminate technology is limited to Baltic birch plywood, which I've found very useful. It's inexpensive, mills well, is available in a number of thicknesses and is dimensionally stable. You can either paint it or apply a veneer to give you a beautiful and environmentally friendly (green) result.
I've found the sticking point in making a camera isn't in the woodworking, but in the various small bits required to allow movements and the ability to fold. For that you'll find yourself getting interested in acquiring machine tools and finding less and less time for making photographs.
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Anyone can appreciate a fine print. But it takes a real photographer to appreciate a fine negative.