Svhools are a minefield. Applying is just like soroity rush. Some schools have catchments, some don't. Helps if you can join an affiliated church. If you find a school you like, you can then ask them for their admissions policy. Some will have it on their website.
Funny, I'm from Chicago too! Grew up there (up north) but ended up in NY after college.
We're looking at reception right now -- he's only 6 months old though. But I've heard that the sooner we get him on the waiting list somewhere, the better. But I've also heard we're a bit behind, even at this early age!!
If you are looking at state schools, you apply about a year before entry. If you are looking at private, then I think the rules are different and the sooner the better. But, I don't have any experience with private so can't really advise there.
I'm a big believer in the league tables. Not really so much as an indicator of the quality of the head teacher or any of the other staff, but more so they tell you whom your child will go to school with. And I think that is very important.