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).