I did a quick search on the MLS for properties in Farmington and Farmington Hills for homes with at least 3 bedrooms and only three popped up that were $1,300 or less. There isn't anything available with a finished basement for that amount.
Click on the link below and you can view the three (3) properties.
If you would like to be set up on a daily updated search for properties, then contact me and I will set that up for you. Maybe you can expand the search to other areas as well.
Thank you and Good Luck!