Okay I think we've had enough discussion about used mattresses. I have one more piece of advice to share:
Michael, before you start buying everything to furnish your rental, I think it's very important to understand who your target market is and figure out what would appeal to them.
To give you an example, I was looking at short term rentals in the heart of Santa Fe, NM. Most of the tourists there come from Texas and California. They are usually older (in their 50s and 60s) who enjoy the opera, museums, art galleries, festivals etc. and many of them bring pets with them. Many of them are also repeat customers who come to Santa Fe every year. It's not much of a tourist attraction for young families and kids so I wouldn't have to cater to that demographics. Now, "Charm" is a HUGE thing in Santa Fe, a rental with southwest charm would stand out much more than a rental without any charm. These are tourists who appreciate nicer things like bedsheets with high thread counts and handcrafted solid wood furniture. These are people who are probably used to staying at 4 or 5 star luxury hotels and would not want $1 shampoos. Also, furnishing a traditional adobe style house with modern looking IKEA furniture would probably feel odd and would take all the charm out of the house. The property manager I was working with at the time also provided a bottle of wine for all the guests at the beginning of their stay, which worked well.
Since you live in NY, your target renters are probably a lot different but I think it's still important to consider what type of place you have, in what neighborhood and what kind of tourists you are hoping to attract.