You may want to talk with a Stucco/Plastering Contractor.
There's only a few of these in the business, and you'll find that the right contractor with experience on old stucco homes will make all the difference. Do a google search for Chicago + Stucco and you should find you a few experienced contractors, but don't hesitate to use the good old phone book or get referrals from neighbors with stucco homes. A lot of the great stucco contractors are "old timers" and have plenty of business without the internet.
There's a huge difference between stucco and a lot of the modern finishes that mimic a stucco finish (refered to as EIFS (Exterior Insulation Finishing System). Stucco is actually a 100% natural material and is one of the "greenest" siding materials you can get. It's a type of plaster that is extremely resilient (made of a lime mortar) and is a very good exterior siding in our climate. I grew up in Andersonville, and Andersonville has some very nice historic homes and buildings. The last thing you want to do is reduce the character of your building by changing the siding material. Besides, you'd be hard pressed to come up with a material as durable and serviceable as stucco.
If the original stucco has damage or cracks, it likely can be repaired at a very reasonable cost. Contrary to most ideas about stucco, the finish color can be changed, but not with paint. Stucco should be colored with a limewash or engineered coating to give it it's color, and thus an experienced stucco/plastering contractor should be consulted. They should also be able to advise you on traditional color palettes. I own a Historic 1893 Stucco Four Square and love the durable nature of the finish. It breathes and doesn't create moisture issues, expands and contracts with temperature and humidity changes, and is overall one of the best sidings you can imagine. When I bought my home, I was very concerned about the durability of the existing Stucco (it was, after all, 100+ years old). Imagine my surprise when it took us over and hour to drill through with a 4" diamond coring bit to put in a vent. It also burned up our first $100+ drill bit!
The previous respondent is correct. Don't go with a EIFS system that mimics stucco, this is not the same and can create BIG problems if improperly installed. By the way, Installing a new stucco finish is VERY cost prohibitive and this is one of the reasons EIFS was developed. Consider the original stucco a "luxury" material.
For more assistance, you may also want to contact the Edgewater Historical Society, 5358 N. Ashland Ave. - Chicago, IL 60640 - (773) 506-4849. I'm a Historic Preservation Commissioner in my town and our commission is always open to giving free, informed advise to a homeowner with an older home. I'm sure they would be pleased to offer assistance. In this case, you may save on your budget and get the WOW factor you want.
Best of Luck!
Keller Williams Chicago Consulting Group