@Nathan Richmond
The first step to transfer the unit into your name, a transfer of ownership form which your Housing Authority will provide. Are you planning on starting up a new lease? If so, inquire on the rules on Rent Increase Request from your Housing Authority, some HA's increase after one year of lease. Also find out how far ahead of tenants Anniversary month will you have to submit a request. Most HA's accept request as long as it has been a year but a few requires submission 60 days before Anniversary month(which is sometimes not the same as lease renewal month).
Search unassisted units 2miles away from the address to see how much the rent in the area is going for so you can have an idea how much to request( section 8 will not approve if your unit is the highest rent in the area). Also, inquire on the payment standards based on the number of bedrooms, that may affect whether or not the increase will fall on the tenant or be paid by the HA.
I hope this helps, you can always inbox me if you need help.