Large format printing is a dark art. It has been discussed here numerous times.
Basically, you should talk to whoever will do the work first, and find out what their file format preferences are. If you care about what colors you actually get, print up a small sample first, because about the only certain thing is you won't be able to predict the output based on either your screen or your printer.
If you wan't to be able to look at the image from a couple feet away and think it's sharp, then you need about 100 to 150 dpi in the full sized artwork.
You can print on self adheasive vinyl. I don't like the way it looks. I think I would print on paper and have it single surface laminated to a thick semi-gloss plastic, and then rubber cement it to the cabinet. Kinkos doesn't have that kind of equipment. It will probably cost $100 a side to have it done at a service bureau.
Or maybe just print it on paper, glue it down, and protect it with semi-gloss polyurethane. If you do that, keep your sample, and test your finish on it first.
Bob