It's great that you're looking to start investing in real estate! I actually got my start in real estate by buying a 3br/2ba townhouse in the NW suburbs (Streamwood). I lived in it for one year so I could take advantage of the low down payment and interest rate and then began renting it after 1 year of ownership.
For the deal you are looking at, a lender would not factor in rent from other tenants when approving you for a loan. The only way another tenant would help the approval process is if they were co-signing on the loan. Typically, lenders do not recognize rental income on a property until it has been owned for two years and the rental income has been documented on the prior two year's tax returns.
Here are a couple of options you may want to consider:
You could purchase a duplex or triplex. You would live in one unit and rent out the others. I know you are from Elgin, and there are lots of cheap duplexes, triplexes in Elgin. I actually just purchased a fourplex in downtown Elgin (closing in two weeks).
Another option is purchasing a townhouse where the payment is $1,000 or less per month (based on your budget). Live in the property for one year and then rent it out. You would want to make sure that the homeowner's association allows rentals. You would also want to do an in-depth financial analysis regarding current rents for those units, annual expenses, etc.
Hope this helps! Hit me up if you want more ideas of how to get started in this area or would like help analyzing some deals in Elgin.