I started as a pick player, using those felt picks - gradually, I incorporated fingerstyle. Currently, I use a pick about 40% of the time. When I do, the edge of my hand lays atop the bridge, with my ring and pinky fingers lightly curled under the G string for stability. I will slide my hand forward to mute, but I very rarely stray far from the bridge area. I typically use medium picks because I like a little "give". I love the Dunlop stuff, but I see them as a luxury since they cost so much more. Because I switch between pick and fingerstyle within a song sometimes, the pick frequently winds up on the floor or on top of my amp, and has a tendency to disappear - hence the frugality factor.
With my fingers, I don't restrict myself as much, but I still prefer to play on top of the bridge pickup, anchoring my thumb on it. I find it is easier to finger-mute (play ghost notes) there. For more wide-open Entwistilian stuff, I move towards the neck, sometimes playing on the fingerboard and anchoring my thumb on the edge of it.