> should I implement the Monad, Applicative or Functor type class?
I struggled with this when I first learned Haskell. The answer is "yes, if you can". If you have a type, and you can think of a sane way to implement `pure`, `fmap`, and `bind` that doesn't break the algebraic laws, then there's really no drawback. Same for any typeclass. It gives users access to utility functions that you might not really have to document (because they follow a standard interface) and you might not even have to maintain (when you can just use `deriving`).
Doing so will let you/users write cleaner code by allowing use of familiar tools like `do` notation, or functions from libraries that say they'll work for any Monad. It saves you from coming up with new names for those functions, and saves users from having to learn them; if I see something's a Monad, I know I can just use `do` notation; if I see something's a Monoid, I know I can get an empty one with `mempty` and use `fold` with it. As long as it's not a really strange Monad, and it doesn't break any laws, it probably just works the way it looks like it does.
If you can define `bind` et. al., but it breaks the laws, it means the abstraction is leaky - things might not work as expected, or they might work subtly differently when someone refactors the code. Probably don't do that.
If you don't implement a typeclass that you could have, it just means you might have written some code where you could've used something out of the box. Same as going through old code and realizing "this giant for-loop could've just been a few function calls if I used underscore/functools or generators".
That said, it's not too common to stumble on a whole new Monad. The Tweet type probably isn't a Monad - what does it mean for a Tweet to be parameterized on another type like `Int`, as in `Tweet`? What would it mean to `flatMap`(`bind`) a function like `Int -> Tweet` on it? A Tweet is probably just a Tweet. On the other hand, it's a little easier to imagine what a `JSON` might be, and what applying a function like `Int -> JSON` to it might reasonably do. Or what applying an `Int -> Graph` to a `Graph` might do.
Most Monads in practice are combinations of well known ones. Usually you'll be writing some procedural code in IO, or working with a parser, and realize "I'm writing a lot of code checking for errors", "I'm tired of explicitly passing this same argument", or "I need some temporary mutable storage", or some other Effect - so you wrap up the Monad you're using with a Monad Transformer like `ExceptT`, `ReaderT`, or `StateT` in a `newtype`, derive a bunch of typeclasses, and then just delete a bunch of messy code.