It depends a lot to the local regulations.
Transportation is a relatively easy part, but it solely depends on the regulations. If you are taking him with your car, the best way is to give him a mild sedative or something similar. Dosage is very important here. Weight and age are essential to find the correct dose. Consult a veterinarian about it.
Most airlines and trainlines accept the animals under certain conditions. You need to make sure that he is microchipped, and has all necessary vaccinations. Even though air transport seems faster, it is also more prone to delays. I had a few friends who had to take their cat on a connecting flight and it was quite hard for them. You can have the cat dig some soil by the road but you can't prepare a litterbox in the airport. Besides, if he is allowed in cabin, he might start bursting his lungs meowing, annoying all passengers.
Settling down to a new place requires some planning.
Cats have an internal compass that guides them to their home, but it doesn't work 500 miles. Most they can do is a few km. So, he won't try to get back to Illinois. Yet, since his internal compass would be reset, it would take him a long time to stroll freely in the neighbourhood. Make sure that the cat is microchipped and has a collar with a nametag. Easy-break collars should be around $5. If the collar is not easy break, he might strangle himself if he is caught by a fence or a branch. In this way, if he is lost, someone will see the nametag and contact you.
Cats are more attached to their surroundings than to their caretakers. If you have an old couch that your cat likes for some reason, take it with you. You can discard it after a few months. The same goes for carpets or mats as well, whatever your cat seems attached, take them with you.
The first few weeks is the hardest for settling in a new place. Try not to let him out until he stops being jittery inside. If both inside and outside freaks him equally, he will be more unpredictable.
I hope this helps. This kind of adoption is the best and most natural adoption. I am very happy that you take the extra step and decide to take him with you.