First off, you won't see the flickering, and if it's a problem after you put in the rectifier, you can just use an electrolytic cap to smooth the DC. You'll want to set the handles down to about 8-9 volts AC with the bridge rectifier, as the DC output will be around 1.4 times the AC RMS value. Also, with a bridge rectifier, you'll have 120hz pulsating DC, as both sides of the waveform are passed by the bridge.
Digikey is my go-to place for cheap electronics. They are cheap, have tons of stuff, and shipping for small orders is only a couple of bucks.
