Illinois requires you to purchase a FOID card from the state police to legally own firearms and ammunition. It is $10 and good for ten years and I think they no longer take paper applications. It has to be done online or over the phone. You need to have an Illinois DL or state ID card first. There are no nonresident FOID cards.I am told that the long backlogs that used to occur are a thing of the past and most people get their FOID cards within a few weeks of applying.
If you are a black powder shooter you will need a FOID to get black powder or Pyrodex.
You will need it to buy powder, and primers if you reload.
You will need it to buy ammo.
Illinois does not recognize the federal rules on antique firearms and muzzle loaders. If it can go bang, it is a firearm, regardless of age or how it is loaded.
Illinois also has some peculiar rules about airguns. Airguns that are over .18 caliber and shoot > 700 FPS are firearms.
72 hour waiting period for handguns and receivers. 24 hour waiting period for long guns. Must call in NICS check. Waiting period seems to start when you make the call. Waiting period applies to private sales.
After you get a FOID card you can go take the concealed carry training class and apply for a concealed carry license. I see it mostly as a license to leave a gun in your car when you go out since there are so many places you can't carry, so I never bothered to pay the $150 license fee plus the training cost. Generally the training is 16 hours but you can get credit for previous training. The training is controlled by the syllabus put together by each individual instructor.
There are no statewide bans on much of anything firearms related other than such things as dragon's breath ammo and other stuff few people really care about anyway. A few localities have some restrictions but state law bans any new restrictions.
No bans on number of firearms allowed or amount of ammo, although there are the normal fire code rules about amount of powder and primers allowed, but not all localities have enacted fire codes that would apply.
No full auto or short barreled shotguns.
You cannot buy a short barreled rifle but you can make and possess one after you go through the federal tax stamp routine. I think you have to have a C&R license to make the SBR. I am not sure if you had an existing taxed SBR if you could legally bring it here if you had a C&R license. It's a strange situation and you need to look very closely at what the law actually allows.
I am not 100% sure but I don't think there are any special restrictions on AOWs. probably you want to look closely at that if it applies to you and not rely on my potentially faulty understanding.
(I am knocking on wood as I type this)