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If it weren't pouring here, I'd set my automatic-photo-taking-gizmo to take 15 second exposures (longer than that and you're going to get star trails, which you may not want). And have it take continuously until the battery ran out, or it got light, whichever came first. I'd start an hour or so before peak (or three hours before dawn, whichever came first).
I'd try ISO 3200; might need 6400 at that short exposure. A test exposure or two will tell.
I'd use my widest lens (16-35 f/2.8 II) at f/3.2. You'll be surprised how little of the sky even 24mm will get, and you want as much sky as possible.
The Milky Way makes a good background, if your FOV is wide enough.