The cabinet I built was a plywood box with the inside lined wth spanish cedar & the exterior covered with mahogany panels my thinking was the plywood would act as a barrier between the two wood species, but it did make for a rather heavy cabinet. You could also just use a hardwood plywood for the exterior & lined interior with cedar. Wood will expand across the grain more than the length so I started by applying the spanish cedar on the top & bottom first, I have the grain running front to back & left a small gap about an 1/8" or a little more on each side to allow for expasion, then came the back piece cut it snug between top & bottom & with the grain running top to bottom with same gap on each side, then applied the side pieces I used cuople of small brads towrds the center of each end on the top bottom & back, the back piece will keep the top & bottom flat against the case the sides will do the same thing plus keeps the back edge flat I did put a small amount of glue towrds the front edges of the sides & a few brads on front & rear edges of the sides, I used titebond II wood glue and haven't had any problems. Once the wood is seasoned and humidity stablizes the spanish cedar shouldn't move much more.
The minimum thickness I'd use would be 1/4", I resawed some 1" thick rough stock in half & it was a little over 3/8" thick once it was surfaced my original plan was to use 1/2" thick.
An overlay door will be easier to seal than the inset like I used with the overlay door you can apply weather stripping around the interior edge of the door to make a good seal in my case I had to hold the cedar lining back to allow for the thickness of the D shaped foam that I used, you can use pretty much any cabinet door type hinge you will just need to take into account the cedar thickness as part of the overlay dimenision if you go that route the 35mm concealed type hinges are available with overlays from 1/2" up to 1¼". Hope this helps you out some