Everyone that has commented is/has done great work and is smarter than me...but I want to offer one alternative piece of advice.
The one reason I would say it makes sense to buy your artwork BEFORE building the cab is - if you know you want to build as close of a replica to a real DK as possible - buying the correct artwork will force you to. If you building something off you'll have to redo it, but the end product will be closer to the real thing. And building an essentially perfect replica would let you more easily add authentic DK parts in the future if that ever comes up. (lets say a cool original DK marquee pops up on eBay for example!)
All that said, those aren't major things and I'd worry more about what's easiest and best for you.
This was my idea from the beginning. I do have something to confess... I picket up original marquee, screen bezel and control panel overlay on Ebay last night..! I don't want to come of like a ---meecrob--- and go against all the advice, but I still think that building from those make sense. Anyway, its not often you find someone on Ebay who ships big things like that to Sweden so I grabbed them when I had the chance. Worst case I'll just put them on my wall like awesome art!
I still go back and forth on the screen thing. I really would like to avoid a LCD. I went to a cafe that have some arcades today and the owner gave me tons of tips and he let me look inside one of his machines. I learned a lot! He kind of pushed me towards looking for a real arcade monitor and going the whole JAMMA and real PCB route. That is way overkill for me right now but maybe something in the middle. A PC CRT would probably look great to me. Easy to hook up to my PC running MAME right? Only think is I have no experience opening CRT's and I know it can be dangerous with the high voltage.
I looked around for wood today and it seems like I can find plywood that's 9/16. Also my step-dad have a friend who have a super big industrial laser-cuter that could cut most of the pieces for me. We will look into that when its time.