The only type of dehumidifier that is any good at all during the winter is a fresh air ventilation system. Mechanical and chemical dehumidifiers are not only expensive and bothersome, but they cannot generally reduce the relative humidity to less than 50 per cent -- not low enough to keep frost off the windows.
In the summer, a dehumidifier in the basement may be useful if ventilation cannot keep moisture down to acceptable levels. For this purpose, find the simplest one that fits your needs; they all work equally well. You won't want a sack of dripping chemicals in a lush basement living room; nor should you invest in a beautiful piece of cabinet work for storing spare tires. Consider whether you need it reliable and automatic to protect valuable storage from mildew.
A properly sized air conditioning system will serve as a dehumidifier. An oversized air conditioner will cool the house, but not dehumidify because it is not working all the time.