I recommend looking at REALTOR.com for current information that comes directly from our Multiple Listing System. On the home page of the site, click the "For Rent" tab and enter ZIP Code 60632.
On the results page, make sure to click through all of the housing types tabs to see everything that's available. Also, set the "sort" feature to "Price: Low to High" so you can work your way up to a unit that meets your needs at the price you can afford.
I just did your search a moment ago, and it produced 16 results. You might try searching other nearby ZIP codes for more properties.
As my colleague mentioned below, it's always best to have a broker represent you. Chicago has a very specific Landlord and Tenant Ordinance that outlines the rights and responsibilities of landlords to tenants and vice-verse.
A good broker who knows the neighborhood can make sure you and your landlord don't run into trouble with the ordinance. You can use REALTOR.com to search for a broker in that area.
You can read a summary of the ordinance for yourself online at http://www.cityofchicago.org/content/dam/city/depts/dcd/gene
Please note that right now there might not be as many units available as there will be in the springtime, since Chicagoans tend to move in the warmer months. Good luck in your search!
Don Pasek, CIPS, TRC, ADPR
Omniterra Real Properties