Someone with ambition, this is rare lol. Have at it man, so far you've got the right ideas.
The fan controller will power and dim the LEDs, I've done this before. But I wouldn't advise putting both fans and leds on a single controller head (I don't think you'd do something like that). My lights are plugged strait into my MB fan headers because I didn't see a need to dim them.
Another option is to get LEDs with dimmers built in. The strip lights are a great idea (that's what I used) and the multicolored strip leds have a remote switch/dimmer that comes with. I think Amazon has them for fairly cheap at decent lengths.
You asked about desk thickness, I assume you mean depth of the enclosure? I wouldn't make it to much deeper than the thickness of the graphics card mounted on the MB (the tallest thing on the board), most everything else can lay flat and fit inside. You don't want an overly deep box because that's a lot if extra air space you'll have to cool and move air into/out of. Keep it as shallow as you can without getting in the way of parts. Two if the builds that I've done are 8inches deep, that gave his plenty of room for working inside and placing parts without making a giant hot air box to cool.
My box is actually a bit shallower, but it works for me.
Another thing to consider is filtration. Cleaning the air before it enters your box will save on west and tear. Oddly enough computers hate dust lol. So fitting a small filter into your intake never hurts.
Side note, I did not intend to out my mouse pad over the glass top.... It just felt comfortable to rest my hand there. I move it over every time I have company and I turn the leds on and let her shine