Any information on how I can approach this here in Chicago, would be extremely helpful.

There are a couple of ways you can get started in RE; the most common approach is house-hacking.

I think your househacking approach will be a great strategy in most areas.

Especially depending on your approach and if you're ok with appreciation and not cash flow (older houses will have maintenance and newer houses have hefty HOAs and MUDs). 

Those are the three ways that I know that you can approach the decision.

It is just my laypersons understanding of the law and how I might approach a similar situation.    

Zillows great for hypothetical situations but today's active listings in your area may be a better approach to a deeper understanding of the rental rates.

Its always best to get their corrections in writing on the job site, so you can approach them later with the literal correction complete, no further issues.  

Alternatively...Have you approached the seller to  see if they are willing to carry? 

The big downside to the wait-and-see approach would be that if you try to get a first lien HELOC on an investment property they will only give you 75 to 80% LTV whereas if you tried for the first line HELOC and owned it as your primary residence you can get up to 95% LTV.