In my professional life I work in a cabinetshop. Not as a builder anymore, but in layout, design and sales. I started out building and installing though, so I have some experience with cabinets, and I can do all phases of cabinet work from start to finish. After seeing the cabinets in my Safari, though I was just floored at how they were made! They had no backs at all, and the uppers had no backs and no tops. There was hardly any plywood thicker than 1/4". Only on a few large doors did they go to a thick plywood. The weight savings is amazing. We build individual cabinets that weigh more than all of the ones from my trailer, combined.
The only door style that isn't flat that would be that light is a "shaker" style door, or some variation of it, with a thin plywood panel, and a solid frame. For more variation you could also try a mitered frame instead of butted corners. all of these door styles can be made thin, 1/2" or 5/8" for "added lightness".
Weather you have flush-inset doors or overlay won't make much difference. If you are really bothered by seeing things that don't line up perfectly you will be happier with overlay doors, and happier still if you leave a little space between the doors and whatever is next to them. Flush-inset doors must hang flat in a opening that is in a flat plane also for them to look perfect, and with the extremely light construction and the amount of bouncing, and the temperature extremes in a typical trailer they will probably look a little different every time you open the door. I personally like the look of flush-inset doors more than overlay, and the variety of hinges available is much better also. I still am undecided about which way I will go with this, but I'm leaning toward insetting the doors in a beaded opening. The beading makes additional shadow lines around the doors and disguises any unevenness between the door and the frame. It has the advantage of looking really nice too.
The really critical part is to keep it light as possible, and to make it something you will really enjoy. Also, find your cabinet latches early-on in the process. You may need to engineer them into your construction depending on what you like and what you can accept.
If anyone has any questions about cabinetry construction it is what I do everyday. I would be glad to help anyway I can.
Good luck, Rich