Looks like someone has been to MACNA XX. I myself was disappointed, but that's another topic.
Anyhoo, to the OP, if you are willing to solder and know your way around electronics, this shouldn't be a difficult project. IMO with a PICO, lighting isn't going to be of too great a concern because I doubt you are going to keep anything in there that is terribly picky about the light.
Check out that famous site where you bid on stuff. I buy Luxeon LEDs for moonlights and such from a seller called LEDHK (I think). He ships out of HK but shipping is suprisingly fast and the LEDs are dirt cheap... about $15 for 10. A mix of the blue and white LEDs will probably work well. High wattage LEDs require a heat sink. For one or two LEDs, I use a piece of aluminum angle channel for them, with a blob of heatsink grease underneath. I usually use a 3.3 ohm, 5w power resistor in series with the LED and drive them at 5 volts. 5v is a nice supply because you can usually get that from an old cellphone charger you can get at Goodwill for a buck.
I bet with a 3 gallon pico, a strip of 3/32" aluminum (google speedy metals), or even better, stainless steel, with two rows of 5 leds (5 blue, 5 white) would give a very satisfactory amount of light. Of course you don't want a million wires running down to a board full of resistors, so you'd want to run the LEDs in series off a single resistor and a higher voltage power supply...