What size led strip?
I use custom ones made for my other business there is nothing special about them but they are UL and IP65. Any decent RGB LED strip off amazon would work. I think most are 1/2" wide by 15 feet. You can buy quick connects for them to cut and extend around anything if needed. I solder all my connections but this is not needed.
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https://www.amazon.ca/Lights-Waterp...d=1548780903&sr=8-3&keywords=amazon+led+strip)
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https://www.amazon.ca/dp/B07M6D5DSH...&pd_rd_r=a506631f-23e6-11e9-8b12-b5a7828cf626)
Did you route a dado to put them in?
Yes and no.... The LED's in the legs are placed on the steel stand. The wood that surrounds the stand was made 1" larger then the steel so that left a channel or Dato to put the LED's in. I do my best to leave a minimum of 1/2" from the face of anything when lighting things up to help spread the light and cut down on hot spots.
What did you cover them with?
The first layer that is closest to the LED is just 1/8" clear acrylic. it then has a white film placed on the outside furthest away from the LED's (this is to better reflect the light as the cover is black). The last layer is a 1/8" black PVC that is glued to the acrylic. I could have used wood or anything that is opaque but the black seemed to work just fine.