There are several quality contractors to to choose from . On the West end, which is the Suffolk Nassau Border, there is O'Neil and Sons, 516-827-3320. On the Eastern End, there is Aleet Enterprises, 631-987-4645. They are both liscensed and insured general contractors specializing in all phases of construction from foundation to finish.
Good Luck and let me know how it works out!
Also - money is money - you talk with contractors just like you normally would - they can choose to cover their costs up front. you can visit http://www.fhainfo.com/fha203k2.htm for an idea about 203k loans.