I want to write a novel or collection of stories that instil happiness
in the reader in a way that makes them want to pass on that feeling
(think Pay it Forward or 13 Reasons Why)"
It sounds like you want to write a story that is inspirational. Most fiction does inspire in some way. The typical (non-tragic) story goes thus:
1. Main Character wants X
2. Main Character tries to get X, but fails
3. Main Character overcomes personal flaw and gets X
That's usually pretty inspiring in its own way. To take it to the next level where I think you want to take it, you'll probably also want to introduce an inspiring idea on top of that story.
If you remember nothing else from my answer, please remember this: Never make your story ABOUT your inspiring idea. Instead, make your movie about 1 or more characters overcoming a personal flaw that helps them achieve the thing they want most(even if they don't know they want it at the beginning of the story). That's a really abstract description of what I'm trying to say, so I'll give a couple examples of what to do and not do.
"Pay it forward" is a good example of what you should do. If you study the structure of the movie(I didn't read the book, so I can't comment), it's not REALLY about changing the world by "paying it forward". Instead, it is a movie about a broken family and a teacher with a "haunted" past. Only when the teacher overcomes his haunted past, and Helen Hunt's character learns to respect herself, do those characters get what they want: a "REAL" family. The whole "idea" of the kid trying to change the world by "Pay it Forward" is almost incidental to the story.
If you want to write a story that inspires people don't make it about that idea alone. That's too in your face. You want it in the background and let it seep in as part of the story. We as people are jaded and are leery of a story that says "Do this, do this, do this!". Instead, give us a well-developed character or two that must overcome a personal struggle. The character might also be trying to achieve an external goal - that external goal can be your inspiring "idea" as long as it is distinct from the characters internal struggle.
I'm getting really abstract again, so I'll give a tried & true example. If you want to write an inspiring tale about kids standing up to a bully, don't make it the primary(and definitely not only) conflict. Instead, the story could be about the kid or (kids) learning to love and respect themselves. Then, once they've done that, they can stand up to the bully. Or, maybe the story could be about a bully's friend who has to learn it's okay to stand out from the crowd to do what's right. Once he learns that lesson, then he can tell his friend, publicly, to quit being a bully.
Whatever you end up writing about, the key to making people want to share it is that you have a character with a deep desire and a person with an equally deep personal flaw(screenwriters sometimes call it an "emotional wound") that they must go through a deep personal hell to overcome. If your character does that, and at the end is able to achieve something inspiring("Change the world", "save the kid", "find true love", etc...), your audience(myself included) is going to want to shout to the world about it.
Hope that helps.
This is not the ONLY way to inspire someone. This is only a very common way that many storytellers have found successful.