Unless I'm mistaken (& please correct me if I am), removing the ability for a landlord to screen problem tenants would flood the market with problem tenants, thus increasing the eviction rate.

Preparing form contracts isn't an overly complex matter and the amount of time expended to create the contracts can be estimated, so I would suggest trying to get a flat-fee rate over an hourly fee for completing such tasks. 

Discussing with individuals that rent in the area, the level of saturation of units in the area right now is driving prices down or keeping them flat.

Do you pay them a flat fee or an hourly rate?

I am looking for a local reputable property manager/management company in the Chicago area who could work with me in overseeing renovation work, tenant screening and management, and other responsibilities necessary to manage a rental property. 

The siding and rear screened patio were in fairly good shape so we decided to keep them but thoroughly cleaned them via power washing.

I would be the "landlord" and take control of tenant screening, repairs, etc. 

If you plan on keeping the tenants a property manager can help screen them.If you plan on buying out the tenants an attorney or someone that specializes in working with tenants.

Even if you use the 1% rule as a guideline for screening it's important to do an in-depth analysis before making any major decisions. 

Know your laws and learn how to screen tenants.