What kind of transistor do I need to amplify an Arduino's PWM outputs?

I'm planning on having 30 incandescent lightbulbs be controlled by my arduino uno on 3 channels (10 bulbs to a channel in parallel). I've used the arduino before to control a number of red, green and blue LEDs - I used a simple schematic using three transistors. I'm just not sure which transistors to get this time considering I'm running the bulbs from 120vAC and not a smaller DC power supply.

Here's a schematic for what I want to do - http://i.imgur.com/BzhM3.png

I've tried controlling just one incandescent bulb with an MJE3055T transistor but all I was able to do was slightly dim the bulb, not turn it off completely. I doubt the power rating was enough, so I tried wiring two transistors together in a Darlington configuration without any luck, nothing happened at all.

I know I should use more than one AC supply to run this - does that mean I'll also need more than 3 transistors?

Do I just need a transistor with a higher power rating? Would this be the right one?

http://search.digikey.com/scripts/DkSearch/dksus.dll?Detail&itemSeq=106696146&uq=634559326654518595

Thanks!!!

Dennis