Bring snow boots, down-filled coats, mittens, woolly socks, scarves, hats, dress in layers when it gets really cold. We are still slogging through winter.
Get out as much as you can - the Main Library has a noticeboard where you might find leads for events. Ridgeland Common has a good rink with public skating hours. The Lake Theatre is a nice cinema 
www.meetup.com/cities/us/il/oak_park/
Find your tribe.
The Dollar Store in Oak Park is a great place for stuff like cotton balls, knockoff Q tips, name brand cake mix, hair elastics, decent wine glasses. There is a decent Aldi south on Harlem Avenue (stay in the right lane after 16th street and pass the Jewish cemeteries). Checkout is more civilised than Aldis in the UK. Pete's Fresh Market is a nice grocery store in OP.
Get a local realtor to help you find somewhere to rent (or buy) in the OP or RF area (if that is your plan). Oak Park and River Forest are both quite closed shops when it comes to real estate in any form. 'Outside' agents don't get the same leads.
Get Ventra cards for the train and CTA buses. You can buy them in Walgreens and CVS and currency exchanges, as well as Ventra vending machines.
www.ventrachicago.com/how-to/ventra-cards/
People use Uber and Lyft a lot here.
If you will have a car and are planning to park on the street, you will need to contact Village Hall to find out how to do this without getting ticketed.