I did think about perhaps offering to rent to them for a specified amount of time at below market value (enough to cover the taxes) till they can get things figured out.I want to do everything I can so not to come off as a prick.  

Did you do the market research?

Find an investor-friendly real estate agent in the market you want to invest in because a typical realtor is not as familiar with how to evaluate the potential of a property for investment purposes.

You asked about the risks and benefits of using leverage in real estate investing.The reality is leverage cannot be avoided, usually, in real estate investing.The risks are you get over-leveraged and your don't have enough cashflow and reserves to weather a market shift, extended vacancy, or major repair.The advantage is you increase your ROI by using other people's money and as little of your own money as possible.

You still have a month but I do think MTRs in markets with a lot of competition can be a bit harder to get bookings on before you have reviews.

Go to Etsy and search for "rental property tracker," and you will find hundreds of nice spreadsheets to track 10-20 rentals, usually for under $10.Software has extremely helpful features like online payments, marketing syndication (click a button, and your property is advertised on multiple sites), electronic document review/signing, maintenance tracking, and owner reports.

There are some that will post on the Bigger Pockets market place but you'll find tons of them on Facebook.  

waiting and saving capital to purchase when the markets better?  

FYI August is a slow time for the NYC market.

This market is forcing a lot of investors back to fundamentals.