New construction windows in a remodel
I like to use Miratec trim, but there are others that work well. Yes, I think a composite is the way to go. But you could certainly use traditional brickmould as well. Azek makes a #908 brickmould that would never rot. If using brickmould, I'd fur the back out with something so that it was beyond the edge of the window.
I've never tried to cut the j-mould off a window- I'd be a little leary of that. I don't quite understand why they don't have a window without a j-mould.
As far as shimming behind the exterior trim, you don't usually have to, but sometimes it helps to keep the trim from tipping.