Additional detail on the new place: The storm door already has a double cylinder deadbolt. The house does not. I'm deciding if either or both should have one at all.
By storm door, you mean an outer door over your main door?
If so, would probably not bother with a lock at all on the storm door (assuming it is glass?) and only deal with the primary door (assume it is more sturdy than the storm door).
In this, I agree you can make it too complicated and hamper egress.
-john