Seeing your questions and noticing your admission of lack of experience with this stuff, buy yourself an EXTRA piece of whatever you use (MDF or Ply, IMO plywood will be better for you, lighter weight, just as strong as MDF, easier to machine, less dust).
DO NOT laminate your pieces before assembly. If you do this, and you are not SPOT-ON-PERFECT with everything, what are you gonna do? You will not be able to remove the laminate without screwing up your hard work.
When purchasing your laminate, also purchase the cheapest piece of laminate they offer (ask them for it, it'll prolly be some hideous color/pattern they hardly sell or some solid color they get cheap) and use this with the extra piece of material to practice on. Laminating is not hard to do if you've got the right tools and READ THE DIRECTIONS, but practice will be your best friend. I K-N-O-W you will be wanting to not waste time and get to building your cab, but practice will pay off in your final results.
You can do it some other way, of course. I would consider it foolishness for someone without experience to do this without practicing it first. I will probably elicit all sorts of "I did it without doing that, and it worked fine" posts, but if those people were honest, they'll also tell of the area they did that "you can't really see it, I'm the only one who knows it's there". NO ONE does it perfectly the first time. There's a reason people pay good money to have countertops installed. I'm just happy I get a chunk of that money.