The two should work together fine. If this is an Arduino Uno, the Serial port will tie up digital pins 0 & 1, while the LEDs can use most any other two pins.
I'd suggest having a read through our Digital RGB LED Strip tutorial
if you haven't already. This explains the wiring, the code, the whole deal.
You might also have a look at the source code for Adalight, especially the LEDstream sketch
. This is a pretty complex program, but you might be able to pick out the bits that make sense to what you're doing...this sketch works in conjunction with Processing code on a host PC.