1]People who are abusive
2] Come from abusive homes AND make no attempt to distance themselves from their family behaviors
3] Child Molesters
All the above are NOT MARRIAGE ELIGIBLE.
Regarding genetic testing: There are extremely sick children born to young, healthy parents where there is NO history of any type of defect. This is the way of Hashem. But, Dor Yeshorim is the best hishtadlus you can do.