Hello, I'm a mortgage professional.
The maximum you can borrow would be 100% of the purchase price. If he appraisal is higher then the purchase price you can still only borrow up to 100% of the purchase price.
In some areas of NY 100% financing is not available. If your in one of those areas the maximum you can borrow would be 96.5% of the purchase price.
One thing you are allowed to do in most programs is invlude up to a 6% sellers concession to use towards closing costs. So if you were buying the home for $160,000, you could make the sales price $170,000 with you getting $10,000 back to use for closing costs.
There are a lot of different options.
I mainly cover NY but can lend nationwide.
I'm avialable almost 24/7.
If you would like help with this you are welcome to contact me.