Specialized glass cutters suitable for cutting stained glass should always be purchased, cheap cutters available from the local hardware store are not meant for this purpose and will wear out very quickly.
Cutters come in a number of styles; the two most common ones are, pencil grip and pistol grip, some have an inbuilt reservoir to hold lubricating oil for the special cutting wheel. If possible you should try the different styles before buying.
Glass cutters do not actually cut the glass; they leave a score line when is then separated by using either special pliers or by manually snapping the glass along the score line.
There is not much difference between the two styles, pistol grip cutters require less pressure when cutting, and it is a matter of personal preference. If you have to cut a lot of fusing glass then using the normal pencil grip cutter can be quite tiring.