OP, are you still there? Obviously lots of us in the area that have our favorite methods of transport in from the airport. In addition to @Nova10 suggestion of American Cab, after years of American, I’ve started taking 303 taxis. http://www.303taxi.com/local/evanston.html. With either one, you need to call for a pick-up after retrieving luggage. I’ve not waited more than 20 minutes in recent months, but longer waits are possible as @MaterS says. As stated, don’t take a Chicago cab either in from the airport or from Evanston to Chicago unless you want to pay the premium prices. I would not consider any form of public transport with a cello - just too much. If it was me, I would rent a car at my arrival airport and drive in to Evanston, then on to Ann Arbor.
@MaterS - which limo service do you use??? I’ve not tried Uber from ORD, maybe that’s an option.