It's traditional to serve a whole fish on New Year's Eve and save half for the next day. The Chinese word for fish is similar to the word for plenty, and saving part of the fish for later consumption insures symbolic abundance for the future. In true Chinese fashion, buy the freshest fish you can. When exploring the options, insist on a fish with clear eyes and a clean, not fishy smell.
As with chickens served during this time, it's important to keep the fish whole, with the tail and head intact. The body of the fish represents family unity or togetherness. If you're serving guests, place the fish on the table facing them as a sign of respect and welcome.