Well the arduino nano is a good starting point. It has 6 PWM outputs, so with a mosfet switch you could dim and individually control each set of LEDs.
As for power supply, you would need two separate voltage levels. Then you could run three chains of spectrum filler LEDs off one voltage in parallel, and the other two chains of white LED mix off the other voltage in parallel.
After you find out what voltage you need for the two chains, you can source a power supply of digikey or mouser. I think you have a good start. I completed my own DIY setup using an arduino Mega 2560.