Just as a start, figure out what type of business you want to form, i.e. sole proprietorship, corporation, partnership, LLC, etc. Then check with your state licensing board that governs contractors for specific requirements and further guidance.
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In terms of insurance, you will likely need to consult an insurance broker. At the very least, you will need to purchase a commercial general liability policy that is appropriate for the type of work that you want to perform. As far as licensing, you will only need a license if you are doing home improvement work. If you are not going to be a home improvement contractor then you do not need a license. Of course, if you are going to be a professional that requires a license that is a different story (plumber, electrician, etc.). Each county in NY, and some other municipalities (such as villages or towns) have their own licensing requirement for home improvement work and you must be licensed in each area where you are going to be working. The other thing that you really should do is retain a construction attorney. Construction is a very complex legal world and is one business where you will encounter legal issues on almost a daily basis from drafting contracts, to signing lien waivers or filing your own liens. It is better to have an attorney on hand from the beginning to walk you through the legal issues and, hopefully, prevent problems down the road.
In terms of funding, there are a variety of angles you may wish to take. The most obvious are bank and small business loans. If you have experience and a solid biz plan/potential clients, this might be an avenue you can avail yourself of. Also, you may, if applicable, want to look into minority owned business grants. Another route, you may explore is taking on private debt/loans from third parties or private investment into your company depending on your short and long term capital needs (there could be important legal precautions and requirements you should be aware of before going this route).
I hope this helps and good luck with your venture.
Disclaimer: This answer is for informational purposes only and does not constitute general or specific legal advice, nor create an attorney client relationship.
You probably want to start an LLC. If you are going to do home construction in westchester, you will need a license from Westchester county