If you really want to controll each of the LEDs then practically you have to use shift registers, as there are 576*3=1728 pins to be controlled and the pis dont have more than 17 GPIO pins.

Lets assume that we leave out the brightness part (but the approach is same, you would need 1728 more PWM outputs to controll the brightness), then the number of shift registers needed will be 1728/8=216. I would reccomend using the 74hc595 ones as they are cheap and has quit many resources.

So the basic idea is to feed in the state of each colour of each led of all leds as either ON or OFF to all the shift registers (since we are not dealing with brightness now, only three bits for each led is enough) and then latch all registers to display the image.

6-digit 7-segment displays are not very common: Single, 2, 3 and 4 digit modules are much more easily sourced.

Here is one 6-digit 7-segment intelligent display module that can be bought as a kit or fully built - it actually consists of two 3-digit displays on a single PCB, with a serial interface:

It uses a serial input, 9600 baud, 8 data bits, 1 start bit, 1 stop bit and no parity.

Alternatively, consider using a 4-digit module with a colon indicator midway (e.g. from SparkFun) and tack on a smaller-sized 2-digit display module for the seconds.

Modules like the one above are more suitable for a clock than regular 7-segment displays anyway, with the hours and minutes separated by the colon.

Using a smaller seconds display module will increase readability of your clock as well.