how do you guys pick? does your hand rest on the bridge or does it always float, assuming you do not need to mute?
Oviously, you can't lay your hands on the brigde if you are not muting.. And about the pick, al guitar players should learn the basic picking, which is the alternate picking. And that is what i mostly do =) Btw, why did you ask? there are also some other type of picking which i do not know what they call it. There is the Sweep picking, and idk the others! lol!
I like anchoring my palm or wrist on my bridge or right above the strings, gives me a stable platform to tremolo pick.

For picking, it's best to start with alternate picking, because it'd help you develop an even tempo for picking.

Down Up Down on all strings first then the other way

Up down Up to balance things up

then once you become a natural with alternate, try economy picking.

And for building speed, remember this:

Relax your hand muscles, keep it loose and fight the urge to tense up.

If you're hand starts tensing up slow down a bit.

Just remember, speed is the result of accuracy not speed.

Just take things slow, easy, and relaxing.

Practice every spare second you have, but avoid frustration at all costs

and above all have fun.
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i usually anchor my pinky on the pickguard. But i've seen guitarists actually not lean on anything.