Finding the right box is all the work you need to do, BUT that took me months of looking online and checking every store's storage section. Finally I found the perfect box the IKEA SNALIS BOX & LID.
It's completely opaque so no need for worrying about light diffusing and it's a great size. The lid also has a lip which I wanted and it has no branding or see thru stripes like all the sterlizer boxes I considered.
For the lights I used six adhesive ENERGIZER LED TAP LIGHTS in the bottom of the box.
The only time it takes is to put the batteries in the lights, so easy! The box cost $8 and the lights and batteries cost approximately $25.
Here's the top of the box.
Here's another view of the box with a good representation of how bright it is. I'm pleased with the brightness, but there is plenty of room to add more lights if you want it brighter.
Here's what it looks like inside with the six lights.