Rotating POV LED Cylinder Using Addressable RGB LED Strips
This is a very ambitious first project, and it will take a fair bit of work to get it to work at all. Here are a few thoughts:


You will need very robust mechanical components to support something tall spinning fast. Ideally you'd put another bearing on the top.
Balance will be important. It would be easier with 4 strips.
You need a way to make it safe, which means enclosing it. A clear acrylic tube would work nicely (and give you a way to mount a top bearing), but it's not going to be cheap, and it may diffuse the light.
I don't remember what the viewing angle of the RGB LEDs is, but it's not great. You viewing part will be, at best, the 45 degrees of the cylinder that is facing you.
Power and data to the LEDs will be problematic. You could push power with slip rings (as long as you filter on the LED side), but I doubt you can push data over it. That leaves you doing something wireless to get the data out there, perhaps 802.11 or 802.15, or something else. Since you need a high data rate for POV, you'll need to do a good job here. 
WS2812 is great, but according to Phillip Burgess at adafruit, in "The Magic of NeoPixels", it's not good for
POV. They recommend LPD8806. Because "the WS2812 ... refresh rate is relatively low (about 400 Hz), and color displays in fast motion may appear “speckled.” ... For POV use, LPD8806 strips will look much better (they have about a 4 KHz refresh rate)."
You can drive ws2812 with the Pi, but
you need a special library to do it, and I'm not sure what data rate
you get.
You will definitely need to write code for this project.