Contact the club and find out when they race. Go down to the pond and see what it's like. Talk to the skippers, ask their opinion on the best beginner's yacht that you will be able to race in their club. Where class rules permit it, building your own yacht can dramatically lower costs. Discover whether the local club holds construction meetings or if there is someone that is able to help you if you get stuck.
Most clubs are very willing to help new members get started.
The AMYA also has a few sets of plans available through the AMYA Ships Store. There are essentially two different kinds of classes. Development classes tend toward encouraging new designs, and One-Design classes tend to focus on restricting development to make all boats as equal as possible. In reality, there is an almost continuous range of types. AMYA Classes have one of two kinds of governing structure.