Shop for a mortgage:
Call brokers, bankers, banks.
Give them your credit score, the % you're putting down, the amount you want to borrow, the Borough it's in.
Ask what rate they can give you.
Do NOT give your SS# until you're really applying.
Even after you start with someone, you're not stuck there. If you can get a better rate elsewhere, or they can't get you a mortgage at the rate that got you to pick them, you can still move on.
A broker can help smooth the paperwork and other requirements. He can explain your choices - even when you didn't know there were choices. I've had good experiences working with brokers.