At the time, just about everything was going for much higher price per square foot and with multiple offers.

As a student without W2 income, you may need to show alternative income sources like savings, freelance work, or a job offer.

Quote from @Ben Fernandez: Make the offer that suits your assessments.

I'm just going to offer my opinion on Arbitrage in general.

At the time, his offer was low, and I had potential plans for that space, so I turned him down.

If someone offered to finance this house to you at your current rates if you put down $250k would you do it?

Here are some indicators to help you assess a buyer's seriousness:Questions: Serious buyers will ask detailed questions about the property, such as maintenance costs, neighborhood amenities, and property taxesStrong Offer: If a buyer makes a strong offer quickly, it often indicates a high level of interest and intent to purchasePrivate Buyers: If approached by a private buyer, ensure they provide a Letter of Intent (LOI) and proof of funds.  

Instead of jumping into an expensive Long Island market with negative cash flow, consider investing in a Texas market like San Antonio, Houston, or DFW suburbs—these areas offer strong rental demand, lower property taxes than NY, and better cash flow potential.

It will depend alot on the number of beds offered and the size of the home overall; do you have enough indoor and outdoor seating for 9 guests?  

But, it may not offer the ROI as other locales, and it may not be "fun" like buying in a favorite vacation spot.2 - The highest ROI folks - Self explanatory, will go where ROI is high and/or regulation low.3 - The second home/retirement minded - These people are looking for minimal ROI but want the house in a specific location because they like to use the property and want it to pay for itself.