Under Wild Shape it says "assume the shape of a beast" you have seen before. Does this mean they can only transform into creatures that have the beast type, such as bear, wolf, crocodile, etc.? Or can they turn into things with other types, like dragon, monstrosity, humanoid, fiend, etc.?
The key word here is indeed beast.
Beast is a defined type of creature within the game, as per page 6 of the Monster Manual;
Beasts are nonhumanoid creatures that are a natural part of the fantasy ecology. Some of them have magical powers, but most are unintelligent and lack any society or language. Beasts include all varieties of ordinary animals, dinosaurs, and giant versions of animals.
Since Wild Shape specifically says
assume the shape of a beast
you are limited to only creatures that have the beast type.
Note that at level 10 a druid of the Circle of the Moon gains the ability to Wild Shape into an air, earth, fire, or water elemental, but it specifically limits it to those 4. This does not allow the druid to Wild Shape into any creature with the Elemental type (such as a Galeb Duhr or Gargoyle).
To be fair they specifically call out that if they are going to use a defined term for Any ruling that it will be capitalized when used as such or else it is merely the word as standard meaning. In none of the printings has there been a use of “Beast” instead of “beast” therefore they are leaving the ruling to the DM instead of saying all of that type and only that type are allowed. Personally when i DM i consider any creature that the character would logically be able to understand the natural role and life of the creature in question, so for example almost all but the most cynical, ignorant, or egotistical (not usually druid aspects) would be able to understand the role and workings of common forest or domestic animals in the region they live. However a camel or crocodile would be alien to a nordic race, a bullette might be normal to a gnomish ground dweller however a roc is just bizarre and unfathomable. In general avoid creatures smart enough to make their own language, avoid beings from other planes unless the druid is from that plane (then swap the lists) or its native to both, and if the creature does not make sense for what your campaign rules feel like they would restrict then don't allow it.