It is important to know if you only need 7 colors from the RGB or do you need to mix colors to create a wider array of colors. If you only need 7 colors then you only need on/off for each "frame". If you want to mix color, you have to create a software PWM mechanism where you manually turn the LEDs on and off real fast and POV mixes the colors. I implemented PWM for 44 LEDs multiplexed x2 but I don't think that would scale up to 200 LEDs. You may be able to run 200 LEDs with 595 chips but know your limits. Don't assume what you build with 10 LEDs will scale up to 200 .. work up slow. If what you really want in the end is lots of colors (i.e. cycle through the hue smooth) then you may want to consider another chips like the TLC5940/41 chips.
Understand power needs - 200 RGB LED will need a 60watt power supply at 5v.
When you look at the price of 200 LEDs on e-bay, it is easy to say - oh I want 1000. When you add up what is really takes in time and money - most people end up scaling back by an order of magnitude. So if you have to scale back your project - know your in good company 