I'm pretty much exclusively pick but honestly I don't have many tips... it just felt natural to me (and that's why I've stuck to it, no failed guitarist here thanks... strangely I play guitar best fingerstyle )
I don't "rest my hand" anywhere, my forearm rests pretty heavily though. Avoid long sleeves for a while too I find it makes it hard to anchor. Always alternate is a good rule to start with although you can play around with that once you're used to it. Remember to practice your dynamics, accentuate certain notes. Learn to play hard AND soft and learn to do both consistently over an entire track.
Find songs which test your stamina, nothing too complex left hand but after 2 / 3 times round your right arm should ache something wicked (I find stockholme syndrome by muse quite good for this, although I step up the tempo a bit now).
As for muting... I very rarely use my right hand. My left hand is my tool of choice for cutting notes short