I personally use LEDs from the auto parts store. I've found these to generally be much brighter than anything you can get specifically made for PC, and sometimes are cheaper. Most of these sets too are meant to be tied together to combine kits, so you can add whatever you want.
Hopefully you keep old PC connectors, and/or have some extra plugs from a modular power supply. I then just wire LED to the 12 volt side of a molex connector (since automotive stuff is made for 12v). For the desk, I would recommend just passing them through a PCI cover in the case. Again use a connector here of some sort so you can disconnect the lights to move the PC when necessary. If you don't have PC connectors, pick up a 2 wire trailer wire connector at the auto parts store they are only a couple bucks.
This is my most recent build using two 12" LED strips (one top and bottom), and that's with the lights on in the room, so it's bright, and plenty of light:
They were brighter ones from the auto parts store, and I believe I paid $20 for the kit.
This was my previous build, it used a LED set meant for truck beds.
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