What's the process to buy a third house with a mortgage?? NY

[Henry Ko]

I have a few questions regarding my plan to buy my third house in Brooklyn, NY. My budget is around $1.5 to $1.8 Million for 1-2 family house.

I currently have an apartment in Brooklyn, NY (my primary residence) valued at around $900K with a remaining $250k Mortgage balance. 
$3200 Monthly payment, I also pay $500 a month HOA fee

I also bought my second home in NJ last year for $375k (valed at 430K Now) with a remaining $280K Mortgage.
$2250 a month payment 

I'm planning to rent out my (primary residence) the Brooklyn apartment and buy a bigger new house as I'm planning on having kids. My income is $300K a year and I don't have any debt except for the two mortgages mentioned above. I also have approx 300K retirement account which I'm not planning to use. My credit score is above 800.

Can you please let me know what my options are? How much down payment do I need to buy a third house?