Belt Driven Fans are typically quieter, pull more air and area more serviceable than other types of fans. If the fan does not come on, it can only be a power situation. Look for the following:
Direct Drive Fans are louder, lower quality and will need to be replaced if motor fails.
Multi Fans in 1 Box have a cover that opens that helps seal the fan from summer or winter eliminates. The problem with these fans are that they don't pull very much air and they are much loader then other types.
In my opinion, depending on where the fan is located, the amount of hot or cold that would come from the small footprint of the shutter is minimal and should not be a very large part of your decision when choosing a Whole House Fan. (We do offer shutter covers).