There are is a huge variety of hiking footwear choices available, from crampon-compatible mountain boots for climbing Everest to lightweight sandals for easy trail hikes and watersports. Finding the right pair isn't always easy. The first question to ask is this: boot or shoe? There is no doubt that hiking boots provide better ankle support than shoes, but they're also heavier and hotter. Experienced outdoor sportspeople sometimes choose use shoes for hiking these days (partly because the shoes themselves are much better suited to outdoor use than they were a couple of decades ago), even if the distance is quite long and the terrain rough, but if you're not certain go for boots.
Next, leather or fabric? Most people opt for fabric when they're looking for really comfortable hiking boots, because they're more comfy straight out of the box, but after a very short period leather can be just as good and even more supportive. It moulds to the wearer's foot and ankle. Leather will also last longer if it's keep oiled and polished but on the other hand it's usually heavier than fabric. The next question is, light or chunky? If you're a hiker who enjoys gentle pathways and rolling hills, your footwear needs are very different to those of a scrambler or winter mountain walker. People who might want to wear full crampons with their boots should take that into consideration and pick something with a stiff sole and good hard edges. And last but not least, waterproof liner or no waterproof liner? A good pair of leather boots or shoes will keep your feet dry whether they have a liner or not, as long as you keep them well oiled (see the Shoe Care page), but fabric boots should have a high quality liner to keep your feet dry. Most boots with 'GTX' in the model name are lined with GoreTex, so will be breathable as well as waterproof.