(plays some power chords and observes)
Usually the finger fingering the root note is the finger that is also muting the next lowest string, and I change from just a 5th to a 5th plus the octave by barring with the finger next to my pinky, however, I pick only the notes in that power chord. When I started learning to play, and was taking lessons, I remember busing my ass to be able to isolate a single string or single group of strings so I could play fragmented chords and solos.
As for picking technique, I usually have my hand near the bridge, and sometimes mute the higher strings with this hand, as I play lots of metal-styled stuff, so I need to have my palm ready to mute. I also use this to my advantage on Jaguars/Jazzmasters by using my palm to stop or allow the harmonic ringing from behind the bridge (3rd bridge palm mute).