I have a long post discussing various addressable LED strips somewhere in my post history, I’ll see if I can dig it up. But I will say, regardless of what you decide to use, don’t order from a US dealer like Adafruit unless you absolutely need it within a week. You pay an enormous markup to not wait.
From previous posts:
WS2812 (branded by Adafruit as “Neopixel”) and LPD8803/LPD8806. These are the chips which allow your LEDs to be addressed individually. Regular single-color or RGB strips don’t have these, and they’re part of why addressable strips are so much more expensive.
WS2812 are cheaper and more compact. They place a tiny little control chip inside of the LED module which takes the signal in the wire, instead of going directly to the LEDs. They function through a +5v wire, a data wire, and a ground wire going in and out of each chip. The way data is sent to them is a little funky, because it’s incredibly clock dependent with no way to mitigate problems, beyond breaking strips up. You will need a separate full-fledged arduino just for driving them, to ensure your clock isn’t off.
[Technical Stuff] They transmit signals by having logic highs and logic lows with different square pulse lengths, rather than anything sane. They transmit the full number of one color for the whole line, 8 bits per color per LED on the strip, then the next full set of color data, then the last. Each chip takes its 24 bits off the front of the signal line, then passes the rest on to the next chip. It goes this way until it gets to the end of the line, where bad things happen if the number of bits doesn’t add up to the number of chips. Then, it transmits a 50 microsecond reset pulse and starts over again, with potentially different values. This effectively makes it very, very sensitive to being even a tiny bit off on clock speed.
LPD8803 or LPD8806 strips work a bit different. The chips are actually separate from the LEDs, and are significantly more reliable, but cost way more and look a little funny up close because you have random black rectangles on your light strip. The 8803 vs 8806 thing is just the number of LEDs it can support, either 1 or 2 per chip. The upside to the huge price jump is that they’re significantly smarter. They get 4 wires in and out. V+, GND, and then a Data and Clock wire. They’re standard serial interface, which means they may be more workable on a RoboRio-based solution.
The big tradeoff between the two is reliability vs cost.
To add on since the price has come down into reasonable range, APA102 is another addressable chip that is substantially newer. It’s branded by Adafruit as DotStar, and they’re basically the best of both worlds, unless you absolutely 100% need only 1 wire for signal, and it comes at a substantially higher cost, at least $10-15/m of low LED count strip. With that said, the chips are embedded into the 5050s so they’re not visible like LPD8803s, and they have a clock wire so they don’t need super particular timings like WS2812s.