You will need to apply for an FOID card as soon as you establish legal residence here. Without legal residence established you can not get a FOID card. Usually IL DL or ID showing your Illinois address. As long as you are considered a non-resident or within the grace period to apply for a FOID you can play by the same rules applied to the rest of Illinois subjects.
I would normally question your sanity regarding the move, but always welcome another body in the fight for 2A rights in Illinois. At least with an FOID card you can still OC in MI (except for the car) .