If you take that job in Illinois you should join Illinoiscarry.com a group working to get LTC in Illinois. We would like Illinois to be a shall issue carry state. The Illinois State Rifle Association is also working for LTC in Illinois.
If you move to Illinois apply for your FOID card as soon as you get your drivers license. It should be issued in 30 days. Find out who your state representative and state senator are. If it isn't recieved within 30 days of when your check clears call your state rep or state senator if they contact the Illinois State Police it will magically appear in a few days in your mail box, if not you may wait for 60 days. If you are in Chicago of course your rep or senator may not be willing to help. As a gun owner you should look at the process you need to go through to just legally own a firearm in Chicago, as well as what firearms are prohibited. It is much worse than the rest of the state. Realize that the Illinois Sheriffs Association has come out endorsing license to carry and all sheriffs, I understand, except Cook County Sheriff.