Great topic.... I'd probably do what I do in my vehicle which is sit with my hands on the steering wheel until I have some interaction with or direction from the LEO.
As for entry into my vehicle/home I say come on in. I have nothing to hide so if they want to sift through my dirty undies have at it :)
Luckily, I haven't had many meetings with LEOs over the years but when I have they have been positive. I treat them with respect just like any other person I encounter and things go well. The climate these days with respect to police has really taken an unfortunate turn in many instances. It's the classic example of a few bad apples ruining it for all of us. And by "bad apples" I mean LEOs and civilians.