Angle depends on the type of cab, but also your preference in addition to that.
You could have it nearly vertical, like the monitor on an Asteroids or Williams cabinet.
You could also lay it back nearly horizontal, like a Pacman cab, or anything in between.
I always liked the Nintendo vertical face glass, coupled with the laid back monitor, so that's what I currently have.
Mine only leans back about 30 degrees though.
I've used both methods.
The shelf method is easiest, but I would only use it for a TV, or a monitor without a stand.
If the monitor is on a stand, you will need to block it in, to prevent it from wobbling if anyone shakes the cabinet.
My current cab has a PC monitor in it, mounted vertically to a piece of plywood, that is then mounted to ledger blocks screwed/glued to the cab walls.