Hi Eric. I just moved from Madison Heights so I know the area quite well. With $20k, I would recommend looking at Homepath or Homesteps homes. (Fannie & Freddie) under $50k.
For example: http://www.homesteps.com/address/23083-David-Ave-Eastpointe-MI-48021/39658126_lid
This property is in an OK part of Eastpointe. Very popular rental area. Nice looking brick home. It doesn't have a garage, but does have a basement. Ideally, it would have both.
With 20% down, $9k, your PITI payment would be around $350/month.
The house would rent for about $850
using the 50% rule $850/2=$425
$425 - $350 = $75/month profit
$75x12= $900 per year profit
ROI= $900/$9000 = 10%
This is just an example I found in 2 minutes looking online. It's not a killer deal and I'm sure you can find better. But with $20k, you can buy a house, make minor updates to get it rent ready and still have some reserves left over.
Stick to 3 bed, 1 bath, basement & garage. Eastpointe & Madison Heights are good areas close to you. I'd stay away from Hazel Park, Pontiac and Detroit. Other citys you will have a hard time finding decent homes under $50k.
Let me know if you have any questions
Good luck