Some lenders offer construction loans, or you might consider a home equity line of credit (HELOC) after acquiring the property if you build equity quickly.Long-Term Goals: Consider how this fits into your long-term investment strategy.

With your good credit you can get in to a home for just a few % down.

If you have a class C plus or maybe low B area, you can screen to select the best or top end of tenants in the program. 

You don’t need necessarily need to build credit.

Access to MLS is one of the best reasons for investors to get their license since it's such a low bar to entry and low annual fees for that and access to all dumps on the market.

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

Note: I'll caveat: I believe that other factors should be considered when analyzing the market as well (i.e. economic growth/stability, low crime rate, affordability, etc.)

Ours tenants mostly pay online, 93%, by ACH, debit, and credit card.

I think I would be more worried about the credit than I am about the DUI.

The return on equity is probably very low considering they are paid off so maybe explore refinancing or selling the lowest performing one(s) or your biggest headaches to reinvest in more lucrative deals.I noticed you also used a metric of number of rentals to attain your goal rather than $$$/month.