To my understanding the process is adding my units to a board, waiting for the section 8 representative to contact me when there’s an interested tenant, have an inspection done, screen tenant and have paperwork done correct?

You should have received a default judgement from that court case and that is a public record that any future landlords can see when screening tenants. 

I am a big fan of bnbcalculator and rabbu for quick analysis and screening of properties 

A few things important to our team would be a strong screening/application process, tenant and team communication capabilities, and digital key/gate access integration. 

Make sure your listing is SEO optimized with the right keywords to attract more renters—many property management companies can help with this, along with tenant screening and payment management.

Section 8 is a tool, not a cure-all.It can be a great program if you screen the tenants well. 

Depending on the size of your portfolio, I suggest considering either "PROPERTYWARE" or "INNAGO":Propertyware is ideal for larger portfolios, offering customizable and automated reporting features.Innago has been very effective for me, enabling property marketing, conducting screenings, and managing rent and maintenance requests.

Also, what are the most important metrics you go through during the initial screening of a listing?

Just work your tenant leads, find the best one, screen & lease them, and you're on your way. 

The property includes a screened-in patio and an underground pool.