For financial prosperity the type of food served is usually round to represent coins. Often, the dish will be round beans, like lentils, that will expand when it cooks, symbolizing expanding fortunes.
Many cultures believe anything in the shape of a ring is good luck because it symbolizes "coming full circle" - completing a year's cycle.
Another symbol involves eating sweet food in order to have a sweet year. In some countries people even bake a coin into a sweet cake and the person who gets the coin in his/her slice will have good luck throughout the year.

Happy New Year!!!
Vivian