What would you consider an acceptable credit score? 

They accepted the neighborhood when they leased the apartment.

I only own one rental unit (this one) and don't accept people who have been evicted, but I would not accept someone in a current eviction proceeding either.

You have total control over what you accept as an earnest money deposit. 

I ended up writing that offer and it got accepted right after that weekend.

Banks often require you to have a full set of documents including an accepted offer in their files and the short sale case oened 37 days prior to the auction date. 

Acceptable, lower risk strategy?

Regarding if you should DIY manage or hire a PMC:Many new investors read a couple of posts and then think self-managing their rental property, and avoiding PMC charges, is an easy way to boost their ROI.The reality, is that many of these investors really haven’t taken the time to properly understand what it takes to properly manage a rental property and the corresponding tenants.Here’s a list of some of the requirements to properly manage a rental property:Knowledge of all local municipality, state and federal landlord requirementsIntimate knowledge of all Fair Housing statutesUnderstand all federal privacy laws, as they’ll be handling social security numbers and IDsProper business insurance in the event their computer is hacked and or they improperly dispose of tenant data.Where to advertise their rental, other than ZillowWriting ads compliant with Fair Housing statutesCreating a process to accept calls/texts and schedule prospects to show their rentalA rental application and application fees that meet all local and state requirementsKnowing how to screen applicants to avoid professional tenants and the growing amount of fraudulent dataA lease compliant with all local, state & federal lawsUnderstanding local and state requirements regarding security deposit collection and holdingRent acceptance options for tenants and accounting system to track, including late fees, etc.Plans to handle nonpayment of rent issuesKnowledge of their local eviction laws or access to an attorney familiar with evictionsHow to accept, track and respond to tenant maintenance issuesBuilding a list of handymen and contractors for maintenance and turns between tenantsExpertise at evaluating tenant damages to charge against security deposit when tenants move outResearching local utility requirements to avoid suspension of services that could lead to frozen pipes or flooded basements, etc.

It means the bank has already foreclosed and they didn't sell it at the auction, either because no one bid or no one bid high enough for the bank to accept and they thought they would be better off selling direct to a buyer on the market.

I was reading online and saw that FHA Loans accept auctioned homes but that got me thinking.