The key with MF is to cast a wide net so you have as many options to analyze as possible. 

On mom & pop operations, distance is key IMO.

I agree with several others here....at this point, education is key. 

Having a solid foundation is key, adding significant value to every deal allows you to grow,  I would say with your $50K go out and do a rehab and make $30K on a flip so you can add $20K to your $50K  ($10K set aside for taxes) do it a few times so you have a great launching pad and rehab experience for the rentals. dont buy turn key rentals, always buy below value, and push the equity with a rehab, and right now in the market cycle, only buy great deals, marginal deals will burn you when this market changes.

They were offering it as a turn-key deal with property management and current tenants established.

And as mentioned above, screening is key.

I heard some crazy stories, a guy in my building was blackmailing the owner for key money even though he didn't live there anymore and had illegally sublet it out!

Cash in the bank is one component of that strategy.

I would advise you to look up the turn-key rental opportunities in Memphis and make that your first target (I can think of a really good one, but no ADVERTISING on BP forums!). 

After all documents are signed and payments exchanged, buyers generally take possession of the keys unless a separate agreement has been reached to allow the seller stay in the property for a period after closing.