With a Hyrdrofoil kitesurfing setup there are 5 main parts.
1 The Board: which must have a compatible attachment system (usually consisting of 4 bolts). If you are learning a bigger board with more floatation is advised, to soak up the nose dives. Also a front footstrap comes in handy as you will be doing lots of water starts all over again!
2 The Mast: For learning or foiling in shallow areas a short to medium mast is best. A tall mast is great for racing, or general cruising (and feels cool).
3 The Front Wing: The larger the front wing the better for surfing on waves, with more stability and slower speed. A smaller and narrower wing is best for racing, and general cruising.
4 The Stabilising Wing: The smaller wing at the back of the setup. Usually specifically matched to the front wing
5 The Fuselage: Long rod that connects the 2 wings together, and connects the the mast. Usually matched to both the Front and back wing.