What a fun question!
@Terdin and
@Cuddlebug both give good tips.
I would say the most important thing is "what would be fun for you to write?" What kind of farmer would be fun for you to role play, if the farmer is the main character? What kind of shenanigans do you want them to get into? How will they get out? And riffing off what
@Cuddlebug said, what kind of stories do you like to read and wish you could tell?
Harking back to
@Terdin, the main character's motivation and their conflict are key. What does the main character (probably the farmer) really really want? Then, what gets in the way of the farmer getting what they want? What do they have to overcome to get there? I have a possible second fanfic in mind, and I know what the farmer really really wants, but I don't know what gets in the way. Until I know that, there isn't really a story. Also, the obstacle could be external (e.g. someone really hates the farmer) or it could be the farmer (the farmer doesn't believe in themself or gets in their own way somehow).
And there can be more than one motivation and obstacle, but you need to know what the main one is and which are the side quests. For instance, ET Betsy's main motivation is that she wants love, and her obstacle (internal) is that she's too busy wanting a spouse to really understand who the right person for her is. But she has secondary motivations of being rich and of being a successful miner, and it turns out that a secondary obstacle (again, internal) to her happiness is that she also doesn't really understand how to be part of a community instead of a cog in the Joja machine.
What/who does the farmer care about in the game? Which NPCs do they want to interact with? Are there NPCs they hate, or who hate them? And what does that have to do with the main motivation/obstacle? You might start with what NPCs you especially like and dislike and think about how your farmer interacts with them—and how they help the farmer get what they want, or stand in their way.
When do you want to start in the game? Most people start right at the beginning, when the farmer gets off the bus or sees the farm for the first time. Then the motivation is at least partly "farmer wants to be a successful farmer" and what gets in the way is "farmer doesn't know how to be a successful farmer, plus is broke" but if you want more of a rom com you can start when the farmer meets the NPC or even later, when the farmer gets interested in the NPC.
What's the point of view, that is, what character are you seeing the story from/whose head are you in? Again, for almost everyone this is the farmer seeing the action and responding to the NPCs. But
@Gamer1234556 has done a lot with other characters' points of view and how they see the farmer and Stardew Valley. For my second fanfic, if I ever do it, it might work better to use the most important NPC's point of view, because I see what she wants and some of her conflict. For instance, a Haley x Farmer fanfic might work well from Haley's point of view: Haley's motivation is "wants love", obstacle is "initially doesn't think the farmer is interesting at all" so how would Haley start to see the farmer as interesting? Finally, I don't think I've seen a fan fic on here that is just NPCs with the farmer as a side character, but a lot of fan fic works that way.
What are you adding to the game? You don't have to overthink it but there has to be something going on besides what the game gives you. Ideally, the farmer's motivation is more than "wants to be a successful farmer" and the conflict isn't only "doesn't know how to be," because everyone who plays the game tells that story, at least to themselves. So what story do you want to tell that's at least a bit different from that? (
@Lew Zealand tells stories about farmers who don't care about being successful, and adds hilarity.) Knowing that helps you decide what parts of the game to focus on in the fanfic. For instance, if the farmer's going down into the mines, why is that important to what they really want or the obstacles in their way? Maybe it isn't. ET Betsy's secondary motivation is being a successful miner, so it makes sense to say something about her mine trips in her diary, but she doesn't really care about fishing so it's rarely in her diary (unless she's at the beach being heartbroken and it gives her something to do, or an excuse to bump into Leah and have a long talk). So you might also think about what you like or hate in game. One reason I played ET Betsy as a farmer/miner was that I was bad at mining and playing as a farmer who wants to get good at it helped me become adequate.
Finally, I repeat, what story would be fun for you to tell?