Bovat,
I'm not a loan officer, so take this for what it is worth. If you make 65K a year, then you roughly make around 5,500 monthly before taxes. You need to just look around on places like realtor.com and see what houses are going for in your area, based on what the criteria you NEED is. Then, subtract your 40K, take that number, and take off the three zeros on the end, multiply what is left by a standard interest rate, around here ours is typically 6-7%, so I always tell my clients to multiply that number by 7. When you do, that is what your payment will approximately be BEFORE adding taxes and insurance. I don't know what the tax rate is in NY, but I'm sure it's not cheap, so add to that several hundred dollars to account for those things. Here, our taxes are realitvely inexpensve (knock on wood), and the average person around here pays about 100-150 monthly for tax, but NY I am almost positive is quite a bit higher. Anyway, look at that number and see if that is something you could live with paying, if you see that you may have a hard time paying for that each month, then maybe you'll need to put more of a downpayment down, or look for a house that has fewer wants/needs.
Here is an example:
Price: 300,000
Down Payment: - 40,000
New Total: 260,000
Take 260 x 7 = 1,820 (this will approximately be the Payment and Interest monthly). Add to it the appropraite amount for Taxes and Insurance, for the sake of this I'll say add 680 just so we have a round number of 2,500 a month.
Once again, I am not a loan officer, this is just a hypothetical situation, and just something to think about! Good Luck