These NeoPixel strips have 30 digitally-addressable pixel LEDs per meter and are very affordable and are only 12.5 mm wide, 10 mm if you remove the strip from the casing. This is the strip with black flex PCB, its identical to the white 30 LED/meter except it has a different color mask on the flex strip
There are some things to watch for:
There are 30 RGB LEDs per meter, and you can control each LED individually! Yes, that's right, this is the digitally-addressable type of LED strip. You can set the color of each LED's red, green and blue component with 8-bit PWM precision (so 24-bit color per pixel). The LEDs are controlled by shift-registers that are chained up down the strip so you can shorten or lengthen the strip. Only 1 digital output pin are required to send data down. The PWM is built into each LED-chip so once you set the color you can stop talking to the strip and it will continue to PWM all the LEDs for you.
The strip is made of flexible PCB material, and comes with a weatherproof sheathing. You can cut this stuff pretty easily with wire cutters, there are cut-lines every 1.3"/3.4cm (1 LED each). Solder to the 0.1" copper pads and you're good to go. Of course, you can also connect strips together to make them longer, just watch how much current you need! You must use a 5V DC power supply to power these strips, do not use higher than 6V or you can destroy the entire strip
These strips are sold by the meter!
To wire up these strips we suggest picking up some JST SM plug and receptacle cables. You'll want one of each, one wire is for ground the other is for signal. For the power wire, you will also probably want a 2.1mm DC jack to wire in.