Just use the left and right outs of a pedal, preferably one with batteries, to avoid ground loop hum. You can't damage anything by running a stereo rig, but sometimes a bit more hum is introduced through a powered pedalboard.
About amps. You can use two amps with a real similar tone,
but I like to run one amp gainier than the other, so it makes the
spectrum sound bigger. That way, you have the benefit of one amp complimenting the other.
Another thing that sounds great is to take a two channel amp
with the gain being pretty hot, and it's clean channel very clean.
Mate it with a single channel amp that's set right inbetween
the two tones. Edgy gain.
When you step on the gain channel, the other amp
has a little more cleanliness in it's gain.
When you step on the clean channel, the other amp introduces
a little "bite" in your tone.
This formula for stereo sounds absolutely huge and is touch
responsiveness "heaven"