I'd focus on steady Markets in cities with GROWTH and bet on the long term appreciation.

***Only exception is if an owner has plan & funds to reposition Class D to Class C or higher.https://www.biggerpockets.com/forums/776/topics/960183-what-they-dont-tell-you-about-cheap-rental-properties?

My fear is attracting C or D class tenants (if I can say that) in a C or D class area.

In general, I would buy properties in an LLC that you're going to hold one year or longer and if doing several fixing flips do you want to do them in a C or S-corp.  

Don't look at C+ or B- neighborhoods in Memphis.

Every few days, an inexperienced investor posts on the forums saying "I bought an OOS property and it's a trainwreck; the tenants didn't pay, then they trashed the property, and now my PM is ghosting me"...inevitably, it's a property in a C or lower neighborhood, and the investor got lured into buying it because the cashflow numbers looked great on paper. 

I am sure that they would not mind if you put in a new a/c or roof or remodeled their bathroom (as long as they have another one).You would have to talk with the sellers and find out what they need.

Like everywhere, the market is tight right now AND you'll want to have some knowledge of the area before investing - coupled with your strategy A, B, C or D neighborhood stuff. 

You say you're not banking on appreciation, but you are making a similar bet on gentrification.

I have specific criteria that I'm looking for, eg: they're owned by a real professional turnkey company, my MF Investment shall yield > 2.x DSCR in C or above the neighborhood, and will have no CAPEX issue.