Chris,
Your project reminds me of the Ambilight feature on (i think it was) the Philips LCD TV we had a while back. I would assume you want a soft diffused light, in which case you want to think about the light you will get from the LEDs. Most of our LEDs are high brightness, which means they have a clear lens and a reasonably narrow angle. For example, if you point the LED at a wall, you will get a circle of light more or less. I would suggest using diffused lens LEDs which will give a glow, rather than spots of light. Unless you are planning on putting the LEDs behind a diffuser of course.
About wiring them up, you could put 2 in series with a resistor from 12V. To run them at 25mA, you would use a R = V / I = (12V-2x3V) / 0.025A = 240 Ohm resistor. You could use 220R as it is a standard value, or a higher value if you wanted a lower brightness.
The reason I say 2 LEDs from 12V is because you want to leave a bit of voltage for the resistor. If the 12V is stable, which it usually is from a comp PSU, you could run 3 LEDs in series if you want to reduce the number of resistors. In this case you would use a R = V / I = (12V - 3x3V) / 0.025A = 120 Ohm resistor.
Much of this info is in the wiring up LEDs thread, so have a read of that too.
Cheers,
Carl
