How much you're approved for depends on a few different factors- your credit history, credit score, income, and debt to income ratio are the biggest things. They also try to estimate what your mortgage payment would be and they say it shouldn't be more than 40% of your income. I don't think they go by that standard as much anymore cause I know my mortage payment is a lot more than that! (I work for a bank and am on my second house, so I've been through this a few times!)
You should also check into SONYMA (state of NY mortgage association) - they have a lot of programs for first time home buyers with great mortgage rates, low down payments, and other benefits. When I still lived in NY I got my first mortgage through them and it was great.
Don't worry- I'm sure you will be fine and you'll be approved for whatever you need. Make sure you have your last few paystubs and you can get to the last year or so's tax returns- they always ask for them- if not for the pre-qual, then for the actual mortgage process. Good luck and FM me if you have any questions!