I left Illinois 5 years ago. Legally, you can take anything that is legally yours. You should transport them according to Federal guidelines which guarantee how you can legally take them across state lines. Your easy options are:
1. Let the movers handle it (which is a bad idea).
2. unloaded, encased, and not accessible in your vehicle.
3. Ship them to your destination - NO FFL REQUIRED.
If it is possible transport them yourself. I'd rather store them and get them later than let the movers handle them. Shipping them could get very expensive.
Once you establish residence out of state and have transported your firearms, you can ignore the FOID requirements, but be sure to learn the laws of your new state. You might want to keep the FOID card in case you every need to move back.