Congratulations on taking the right first step, which is getting a pre-approval letter! This makes life much easier for everyone as you consider your options.
There are co-ops that will accept 10% as a down payment in Brooklyn, I have represented some as the listing agent, but yes, this does certainly limit what is available for your purchase. Many co-ops require 20% as a minimum, or even 25% or more.
I would be happy to speak with you to calculate which approach is best for you personally. If you plan to live in the area at least 7 years, owning for most people is almost always a better financial investment than renting.
Licensed Real Estate Salesperson
New York, NY