Welcome @Edward Terres.
I was just recently in your same position.
1, Your debt to income is accurate if your numbers are accurate.
2. Your Down payment and closing for $100k would be more around $6500 for a FHA loan. Use this it was fairly accurate for me.
FHA Calculator ... they also have a conventional thats fairly accurate
3. What is your credit score? If the purchase price is cheap you might want to go HML then use a Homestyle Loan for the rehab and HML buyout. This eliminates the burden and restrictions that comes with a 203(k).
Side Notes:
1. Get prequalified 1st, to get that right property will take about the same time for you to save for your down payment. Lots of competition in the Chicago market, especially for MF.
2. Get a great Realtor, it makes the process do much easier. We went through 4 before we find the right one. This is just my personal opinion but with the price range you are in, stay away from Wells Fargo. They want a guaranteed $3500 commission just for representing you.
3. Im assuming you are getting a fixer upper to gain a little equity. Do a thorough walk-through and map out your design, dont worry about rushing this is your time and your money. Get a General Contractor with a good track record of working with 203(k) financing walk the properties with you. This will be a difficult they dont want to work for free. But there are some who understand and are willing.
4. Babysit you property till rehab is complete. No one cares about it more than you do. NOBODY! Dont be too agitating, learn that fine line and walk it.
5. Many have said it and OMG I can validate it. Sometimes being a noob you plan so diligently and think it might not apply but ANYTHING CAN HAPPEN with a rehab. Contingency funds are important. Plan on replacing roof, plumbing, electrical, hot water tanks, etc. Even if you dont have to. If its in your budget but its not needed, then it can be removed and other amenities desired can be added.
If I have anything wrong someone please correct me.