Do you believe self-showings, where there is little to no human contact, (to build value in your unit or the PM company), until a tenant has paid an application fee, a race to the bottom on your rent rate?  

Now, I did bring a weapon to one of my very rough units because it was vacant and there was reasons to believe there were break ins and people could have been inside.

Ask how many units they manage and how much experience they have.

 We did a 1031 exchange into a 10 unit apartment building. 

In light of the pending Hurricane, I am anticipating significant damage to at least 1 of the units - likely rendering it uninhabitable for a period of time. 

Quote from @Nicole Koch: I think that most people looking for anonymity are basically trying to keep their name off public records so that if they own rental units some psycho cant just look up who owns the property, whats their FB, who is the wife/husband, kids etc.. 

We would also keep a hard copy in the unit. 

Of course, have a professional inspection done that enters each unit and do a sewerscope.

@Eli Kantor The complex I still follow having invested and owner occupied is over 30 years old and has 340 units.

I'd recommend looking for either single-family homes or multi-family properties with 2-4 units.