Unfortunately, there is no simple answer to the fuse question. At least, not if you want an accurate answer. There are as many different types of fuses as there are devices for them to protect. I've spent a considerable part of my career doing fuse coordination design. That is, selecting fuses or a series of fuses to protect circuits and their subsequent subcircuits so that the fuse opens before the device is damaged. People who should know better, tend to oversimplify things into the fast blow and slow blow categories. In fact, there are hundreds of categories. The ideal fuse for a particular device is one whose time-current characteristic curve is identical in shape to the device's time-current damage curve, but shifted down slightly on the current axis.
I'd be happy to provide more info, but usually when I start getting into the technicalities of fusing design, people start to look scared and then back away slowly.