Not Chicago related but we moved to Canada for a year 4 years ago (totally regret coming back so am hoping we will be back out to us or Canada in the next two years!)
My bits of random advice -
Get a set of decent ski kit and snow boots for each person before you leave uk and then you will need a second set so buy that when you are here. Kids wear snow pants and boots to school and then hang them up in lockers and use at recess so def need 2 pairs for when they come home wet.
We colour coordinated each person so one kid had everything blue (hat, gloves, coats etc), one green - made finding kit in the boxes easy and each kid knew who's was who.
Electronics - I didn't get this fully till it was too late. Go round your house now and check every plug/transformer. If it says 110/220 then it can be used over there with an adaptor. If it just says 220 then you need a step down transformer for each one which is bulky and a pita, we needed it for random items I should have just left here (nutri ninja, dyson, one tv etc) but also bought stuff over there we could have shipped over as I didn't work it out till too late.
Tvs all plug into hdmi so no issue anymore with not working over there.
DVDs are region 1 over there so take a DVD player!
If you use apple iOS then you need to change to us store to access American apps and then struggle to update uk ones.
Banks - hsbc let you open one over there in advance if you have uk account.
Transferring money - don't do it bank to bank, rubbish rates. Look at TransferWise or an professional exchange company - much better exchange rate (we took £20000 and the difference between bank rates and TransferWise was £2-3k.
Get all medical records printed by gp (you have to pay but it's not a lot)
Have all immigration docs scanned and save on computer - all birth certs and passports etc scanned and saved. Makes it easier to provide info quickly as you know where it is
Ensure mobile phone is unlocked - then choose your provider over there for pay as you go. Use WhatsApp/face time to speak with uk.
Most schools kids get on bus outside your house and go to school so you don't get the school run as such over there - makes it harder to make friends with other parents. I found it quite isolating from that aspect.
Even though they speak English, it is still like learning to be bilingual as they do use different words and spellings- my kids would be Canadian outside and English inside and I'd be totally confused. I would have to consciously think what I was saying before I opened my mouth, particularly on the phone!
Costco is a major shop over there - get a card here and it works over there. Minimal if any online grocery shopping in Canada, it very nearly tipped me over the edge having to do grocery shops every week!
You won't have a credit rating so may struggle with finance for cars etc - make sure you look into it. Keep wits about you - one main dealer tried to sell us a 1980's shed for more than they were advertising 12 month old ford focuses!
Insurance is done mostly though agents.
Look up car seats if you still need them - that's a whole new issue as U.K. ones aren't approved over there.
When you ship things - have wine!
Make sure a box is full of comfort foods (Heinz soup and beans, spaghetti hoops, Cadbury's chocolate, Jaffa cakes.....for those bad days when you just need a bit of home. Also cordial juices are not easily available over there - koolaid is rank and pure sugar!!)
Also, get some quote from removal companies now - even though work will pay for it it's useful for you to get an idea of how it will work.
Our container came into Montréal and then went on the train to the west coast. I'm not sure what plan would be for Chicago but if coming into Montréal and then down through the lakes you will have a problem in jan/Feb as it's all frozen so can't get though (we got through just in time in Dec but were warned it might be a delay for a few months if that was the case).
Pets - don't need to use transport companies, you can take them on the plane with you for only £150 or so extra. But get vet checks and vaccinations in now to give enough time to be tested for anything extra.
Read up on local bylaws for chosen area - lots of pedantic little rules to fine you by. Can't park on the road for more than 2 days, must clear side walk of snow within certain time period, no hanging washing on balcony etc.