You could write an 'team natsu oc fanfiction' where the OC is from a different dimension and has different cultural norms. This OC could introduce new concepts and ways of thinking to Team Natsu. Maybe the OC's dimension has a different way of using magic, like combining it with technology, and Team Natsu has to adapt to this new form of magic while also teaching the OC about their own magic system.
Focus on character development. Make your OC have a distinct personality, backstory, and goals. For example, if your OC is shy but has a strong desire to protect others, show how they gradually overcome their shyness in the face of danger. This will make the readers more invested in the character.
Happy could be an interesting character. He could be like a sidekick and a source of comic relief during their relationship journey. For example, he might accidentally interrupt their romantic moments or give Natsu really bad advice on how to court the OC at the beginning. Erza could also be important. She could be the one who gives the OC advice on how to handle Natsu's wild nature, as she has known him for a long time.
The OC could have accidentally said or done something that made Natsu feel unwanted or unappreciated in Fairy Tail. For example, if the OC is a new member and got more attention than Natsu in a certain situation, it might have bruised his ego and led to his decision to leave.
In a 'natsu married oc fanfiction', perhaps the OC is a healer. Natsu gets seriously injured during a battle and the OC nurses him back to health. Natsu is so grateful and impressed by her kindness and skill that he starts to develop feelings for her. They get married and the story could focus on how Natsu has to adjust to having a partner who is more calm and collected compared to his fiery self. He might learn to be more patient and she might learn to be more adventurous from him.
Lucy is also a good character to focus on. She has a complex backstory with her family and the celestial spirits. You can explore her growth as a mage, how she becomes stronger in controlling her spirits and her relationships within the team. For example, her friendship with Natsu and how they support each other in battles. Plus, the whole aspect of the celestial spirit world is full of potential for interesting plotlines.
A great fanfiction concept could be centered around Team Natsu getting magically separated. Natsu ends up in a realm where there's no fire magic, and he has to learn to adapt and find a way back to his friends. Gray could be in a world of eternal ice and has to find a way to break free. Lucy might be in a place where celestial spirits are feared and hunted, and she has to protect them while trying to reunite with the team.
One interesting plot could be that Team Natsu travels back in time to the founding of their guild. They get to meet the original members and learn about the guild's true origins. This could lead to some really cool interactions and revelations about the guild's history.
One possible storyline could be that the OC tries to find Natsu after he leaves Fairy Tail. The OC might have a special bond with Natsu and be determined to bring him back. They could go on a journey where they face various challenges and meet new characters along the way. Another idea is that the OC is actually the reason Natsu leaves Fairy Tail in the first place. Maybe there was a misunderstanding or a conflict between them that led to his departure, and the story could be about how they resolve it.