There are three main types of watch glass/crystals. They are acrylic, mineral and sapphire crystal. Each have their own unique properties as well as their own pros and cons.
Acrylic is actually made of plastic and out of three choices available it is the weakest. This however also makes it the cheapest to have on a watch and is predominantly found on watches that are on the cheaper side. You can also find this on watches made for children. I would generally tend to avoid a watch that has acrylic as the crystal as it can be very easily scratched. However, the scratches can be repairable but replacing it entirely would be just as cheap.
Some luxury brands do use acrylic, but they describe it as plexiglass or some other name to disassociate it from the name acrylic. Some people try to find acrylic as it gives a certain vintage look to the watch.
Two examples of watches that use acrylic or plexiglass on their watches are shown below.
This is by far the most common watch crystal that is available. It is said to be a lot more scratch resistant and durable than acrylic. Watches that have mineral are often ranged around the mid-tier when it comes to prices. A lot of people are often happy with this choice and do not see any issue. However, unlike acrylic if the mineral does get scratched it cannot be repaired and will need to be fully replaced. It is very common for people to mod their own watches and change it from a mineral to a sapphire crystal.
Seiko do have their own phrase for the mineral crystal, but instead they call it Hardlex crystal. Although they do claim it to be a bit more durable and scratch resistant than mineral, there is no real proof or evidence to back up these claims.
Most watches that are priced in the upper range of watches will have sapphire crystal. It is known to be virtually scratch resistant. It is said the only thing that can scratch a sapphire is a diamond, however materials that are rated higher than a 9 on the Mohs scale of hardness can also cause a scratch on the crystal. If you need a watch that will be virtually scratch-proof this is the crystal you need to look out for when purchasing a watch. However, due to this they are usually much more expensive than watches that have mineral or acrylic.
Sapphire crystals by itself are a lot more reflective. This is why they are often paired with an anti-reflective coating. Sometimes two layers are added, which gives the crystal an almost invisible look allowing you to fully appreciate the dial and make it very easy to read the time at any angle.
If given the choice spending a bit more to get a watch with sapphire would be recommended in my opinion. Although a mineral would be more than enough for a lot of people, I think personally just having the extra confidence knowing it cannot be easily scratched would give me a much better peace of mind.