The design and layout of your kitchen will largely determine the type of rangehood options you have. This page describes the most common options.
Fixed rangehoods work better than slideout rangehoods as they have a larger air collection area. They generally have less power and smaller air collection areas than canopy rangehoods, but are not as expensive.
Also known as remote fans, silent rangehoods have become more popular, they have a powerful motor which is located away from the rangehood in the ceiling space or on the roof. They are significantly quieter in the kitchen.
Silent rangehoods can be purchased in Canopy, Undermount and Island styles.