Dave,
Try to find a local kayak club, Check at kayak shops and the YMCA or do a google search for NYC kayak clubs. Some will offer classes where you can try different boats. If you can't find a club try a rental shop. Paddle a recreational boat (usually around 30" x 13ft.) then try a touring boat (22-24" x 16-17ft.) You'll find the Rec boats are Fairly stable with a large, open cockpit. Great for fishing, photography or bird watching. The touring boats will initially feel "tippy" till you get used to it, but have a great speed/efficiency advantage for long trips and handle better in rough water. The touring cockpit needs to match your shape pretty well to maintain control.
Try to decide where you want to paddle, I usually run an 8 mile loop in my touring kayak, While my neighbor is just as happy paddling my old rec boat 1/2 mile to his favorite fishing spot. Make sure you know (or have a good idea)what you want before you spend 300+ hrs building a boat. Once you know what type you want, this board is a great place to find out about all the different plans, books, & tools available. - Good luck!