First, you can only receive rifles/shotguns outside your state of residence from federally licensed dealers. No handguns may be transferred to you outside your state of residence from anyone.
If you choose to have a rifle transferred to you by a licensed dealer outside your state of residence, state laws of both your state of residence and the state the licensed dealer is located in must be followed. So, if you can get a dealer at the Iowa gun show to even transfer a rifle to you, an Illinois resident, both the state laws of Illinois and Iowa must be followed. If Illinois state law requires a waiting period, than the waiting period applies wherever you receive the rifle.
A handgun will have to be shipped to an Illinois FFL for transfer to you.