This should do the trick: ebay.com link: SUPERNIGHT 5M 5050 RGB 300 LEDs Waterproof Flexible Strip 44 Key IR Remote

RGB with power supply and remote control for colors. Cut to appropriate size, attach with double sided table, and off you go.

There are several types of LED -- but these will let you control the entire strip in a single color. Each LED has three mini LEDs in it for emitting Red/Green/Blue. If you want control over individual LEDs (make each color different or do effects such as running a pulse of light down the strip that changes color from one end to the other) you'll need to use addressable LEDs. There are some neat things you can do with those, but often require programming an Arduino (which is what I use for the pinduino lighting effects):

From what you describe, the RGBs I linked to on EBay should suit your purpose.

10-12MM, depending if there is a waterproof tube or not.

You can order this one (options shown in picture) if you don't need the water proof tubing (which you may want if you want to tape the LEDs on their top side): ebay.com link: 5M SMD 3528 5050 5630 3014 300LEDs RGB White LED Strip Light 12V Power Supply

Screen Shot 2016-11-26 at 7.44.42 AM (resized).png

Also, the 5050 RGB LEDs often come with a more powerful power supply (5A) to drive the entire strip. You can just get the strip and use a different 12V power supply: ebay.com link: SUPERNIGHT Non Waterproof RGB 5050 SMD 5M 300 LED Strip Light 12V Black PCB

But by the time you buy/find a power supply ($3-5) and RGB controller ($3-5), you end up saving $2-5. Might as well get the whole kit.

Well done and looks great.