First of all - by federal law, the only way to do a person-to-person transfer of a handgun over state lines is to have the uncle transfer to an FFL holder (i.e. a licensed firearms dealer) in your state, who transfers it to you. It’s possible/likely that the local dealer will require the gun be shipped to him by an FFL holder in your uncle’s state, but I don’t know if that’s required by law or not. The dealers will charge a fee for this service, probably somewhere in the $25-50 range per dealer - my local dealer charges $35 as a data point.
According to the nra website, you will need an FOID to possess a handgun, which is a “shall-issue” permit - if you meet the criteria, they must give you one. Note that there’s no concealed carry allowed in IL.
Chicago used to ban handguns completely, but Heller and then McDonald cleared that up. They do require registration of handguns.