There are a few options out there. Conventional loans range anywhere from 5% and up. However to avoid PMI (Private Mortgage Insurance) at least 20% equity or 20% down payment is needed. FHA is 3.5% down and typically requires a credit score of at least 640 (general guidelines, some lenders have different programs).
If you are looking for a condo or Townhome (without Fee Simple ownership) go to https://entp.hud.gov/idapp/html/condlook.cfm to check if the complex is FHA Approved.
I work with a lender that has a program that is only 2% down payment with NO PMI. However, the household income would need to be below $58,000 i believe.
I would be glad to share more info with you or even help you with your home search (the Palatine area is my primary market).