Controlling RGB Strip Lighting?

I am currently planning an RGB lighting system for the bottom of a rolling cart (it's for my high school's robotics team). I will have a linear potentiometer to control the intensity of each color (3 in total), then a push on/off switch to change modes so it cycles through the RGB smoothly with a regular potentiometer knob to adjust cycling speed. This will all be controlled by an Arduino, most likely the Pro Mini from SparkFun.

As for the lights themselves, I am going to use some adhesive RGB LED strip lighting off ebay (China stuff). The specs say it runs off 12VDC and draws 7.2W per meter (I think I will need about 2 meters). I know that the Arduino cannot run them at that voltage, let alone current, considering that'll be roughly 60 LEDs.

Now I finally come to my main question ::) Can I simply use an NPN power transistor for each color and have all the colors connected to a single battery? In general, can your average RadioShack NPN transistor handle a PWM signal well?

Thanks in advance!

for 6 Ft of strip you will want a mofset or Darlington array rated at least 400mA/Ch and for an RGB strip you will need 3x chanels so you could use 3x transistors or just use a Darlington Array

wiring diagram for connecting a Darlington Transistor Array to an Arduino http://fritzing.org/projects/arduino-knight-rider-with-8-blue-12v-led-modules/