I make a lot of maps of Chicago, and I always use EPSG 3435 (Illinois StatePlane East Feet). The City of Chicago’s GIS department also uses this projection.
The State of Illinois government often uses the other one, 3436 (West) because the capital, Springfield, is on that side of the state. I think it would be fine to use either one for Illinois, but Mike Bostock’s response is also a good one (I’m more familiar with StatePlane projections than Albers).