Mounting

So I have made a couple robots but nothing that looks very nice nor clean. I am in the process of making popsci's Atomic Clock Build a DIY Clock that Uses Ultra-Precise Atomic Timekeeping and I was wondering if anyone had any suggestions on ways to mount things to the box. The main thing I want to look really good is the LCD since thats what I'll be looking at it. The hole I cut in the plastic and the screws i drill for the mounting of it have to look perfect. Also, any suggestions on how to mount PCB's in the box?
Thanks in advance!

You obviously want it to look better than the article, I take it?

You'll probably need to have it laser cut or CNC cut in order to get the perfection you need. Expect to pay some money for it, unless you have the tools (where the expense will be setup time).

If you want to come close, then use a drill press for the screw holes, and use a center-locator to position them accurately, based on a template or marked/scribed points on the box. You will probably need an x/y positioning table on the press for this (plus clamps, etc). You could also use a drill/mill machine, if you have it (but I take it you don't have any of these items, or you would know this).

It can be done by hand, if you are willing to take the time. Print out a full-scale representation onto paper (use a CAD program or something similar, where you can lay things out accurately), and affix that to the lid/box. Carefully mark the holes, etc - drill them with the center jig on a drill press. For the LCD hole, use a dremel or model saws to cut a little on the inside of the line, then finish to spec using hand rasps and files (make sure to wear a dust mask when doing this, especially when working with plastics like styrene, pvc, abs, etc).

If you take your time, you will end up with a very nice result.