Yep, i've done this myself. A normal 100W incandescent lamp is around 1500-1700 lumens which is good for a typical room.
When i did my LED setup LEDs weren't quite as efficient as they are now. I needed 30W of white LEDs to get that 1700 lumen output.
I think now you can do it with ~20W.
The cheapest controller is just a mcu/ardunio and 4 mosfets (for RGBW)
It's cheap to just use high wattage series resistors to limit the LED current, and you have a heatsink for the leds anyway so you can bolt/glue them to that. I used thermal epoxy to glue typical 5W ceramic resistors to the side of the led heatsink.
Of course you can get a proper switchmode current limit LED controller if you want, it's more efficient.
Code the mcu to PWM the 4 mosfet color channels (above 200Hz) and your done.
I added extra code to provide IR lighting control, just because it was cool and why not
Obviously you want to put the LEDs into series strings and pick your power supply voltage carefully so it's only 1-2V above the total LED string voltage, that way you limit the wasted power in the resistors.
I had more red leds in each string than white due to their different forward voltage but the total LED voltage of each string was close to 13V for each color. (My psu was 13V)
As far as mixing goes, i have 30W of white and 10W each of RGB, which is great but probably a little excessive for the size of the room. It depends if you want to just "tint" the white or actually illuminate the room in a pure RGB color, which is always fun.