Grew up in Chicago so I've been following this, and I knew he'd win.
The issue is that he wasn't a Chicago resident (he'd spent the past few years in DC, of course, in the Obama administration.) He left some of his old belongings in his former Chicago house, which he claimed proved residency. So one court disqualified him from the race, he appealed it, and finally he was allowed to run.
The thing is, like all cities Chicago has a budget problem. Honestly I thought Rahm was the most likely candidate to be able to do something about it. It might not be what we want (there will be some taxes and borrowing) but, say, Carol Mosely Braun was talking as though we could count on federal largesse, which isn't all that likely. Rahm might be slightly more pragmatic. I just want us to keep essential city services working (police, fire, schools, road safety, etc.) These days that's not guaranteed.