I have
1x 5v RGB LED string that requires around 4Amps 67LEDs
1x 5v RGB LED strip with 180 LEDs which I think requires around 9Amps
And
16x 12V 3 watt G4 LED bulbs
What's the most compact way of powering these lights? Is it better to have a 240v ac to 12 v dc supply then step down to 5 volts? Is there an IC that I can use to make the arduino control and dim 16 12V leds?
For reference this is the sort of space I'm dealing with. No space for anything bigger than 8cmx8cm though there is space for several thin transformers
Led lights use a adapter/inverter/thingy that supplies more or less a stable current for the leds. They don't need to be accurate and can be very small.
You want a stable 12V and 5V and many amps.
I think mrsummitville mentioned everything. Try to find a single power supply with 12V and 5V output (Option #2) that is small enough.