As far as amenities go, I would say a tv that has capability to play music on youtube and / or stream content from my phone / iPad and a microwave. #2.

I have security cameras and my tv on the wall.

New tenants will be moving in soon and they mentioned mounting a flat screen TV.

Make sure you have cash reserves (about 3 - 6 months worth of payment) so you're not pressed about tenant making rent. 

I have not had too many headaches managing the properties, but do not want to press my luck and always prepare for the future.

But maybe you go with just a fire stick or a fire Tv. 

Can you start a new tv show on the auctions?

If Nolo press has a landlord book for NY start there.

There's also a death by Google search to see if the sponsor and any of the individuals had any negative press. 

Sometimes I watch "Hoarders" on TV trying to get an idea of why some do this (my brother was one) and I suspect the only option is to continue monitoring...or, if bad enough, get her out of there.