lillii:
Many thanks for the advice. It's not that I don't want to design a custom board, I just don't think I'd be confident enough to do it as my first Arduino project...
I hear ya. On the other hand, there's no time like the present. Everyone starts somewhere. 
This is exactly where I started, by building a custom controlled for an LED project.
It might be worth it for you to try and prototype this first. Whether you use a stock Arduino board, or you prototype that as well. You don't need much, the Atmel, a crystal with caps (or resonator) and a 3.3V - 5V source. Once you burn a bootloader to it (using a stock Arduino), you've got yourself an Arduino clone that you can program the same way you would any stock Arduino. Pull the necessary lines for an FTDI, at a regulator if you're going to feed the whole thing 12V (for the LEDs) so that you can drop the voltage down to 5V.
After that, just add the MOSFETs where you need them, connect them to the Atmel pins, add the headers for your LED strings and power supply and you're done.