I preferred couples rather than families due to liability and damage.

Not much, but something to keep in mind.They are all good options, I would also recommend a place where you are physically the closest to or can get to easily.

Other lease provisions may apply as well, such as prohibition against causing the LL to incur fines and damages.

The Landlord will verify that the rental is empty of all personal belongings and trash and that there is no damage beyond ordinary wear and tear. 

., property management companies aren’t legally required to carry general liability insurance, but it’s highly recommended for protection against bodily injury or property damage claims.

Central A/C is damaged beyond repair and needed to be replaced, which can't be done economically or with coopperation of the HOA and other neiighboring owners.

Physical auctions.

  $7k damage. 

For instance, said property manager manages maintenance issues, problems that arise during bookings, basically anything that needs a physical person at the property, while I manage the rest?

Assuming your friend has a contract with the management company it sounds like (s)he may be in breach of that and could possibly be sued for damages.