Joey could be an ordinary citizen who just happens to be in the wrong (or right) place at the wrong (or right) time and meets the Batfam. Maybe he's a journalist trying to get a scoop on the Batfam and ends up getting more than he bargained for.
Joey might be really impressed. He could be like a kid in a candy store, wanting to see how all the cool Batfam gadgets work. For instance, when he sees Batman's utility belt, he might be constantly asking questions about what each gadget does.
Well, perhaps Joey is a big fan of the Batfam in the fanfiction. So when he meets them, he fangirls/fanboys really hard at first. Then, as the story progresses, he gets to know them on a more personal level and discovers that they have their own quirks and insecurities just like regular people, which changes his perspective of them completely.
Well, one possibility is that Joey could be in awe of the Batfam's reputation and skills. He might try to prove himself to them, perhaps by showing off some of his own unique abilities from the Teen Titans. For example, if Joey has some sort of special power like telekinesis, he could use it in a controlled way to gain their respect.
In the 'Spiderman meets the batfam fanfiction', it's possible that Spiderman would be intrigued by the Batfam's gadgets and their more brooding approach to crime - fighting. He might try to lighten the mood a bit. The Batfam, on the other hand, could be impressed by Spiderman's acrobatic skills and his quippy sense of humor. There could also be some interesting interactions between Spiderman and Robin, as they are both younger heroes in their respective universes.
Well, there could be epic battles. The Batfam's unique skills and the Justice League's superpowers would make for some intense fight scenes. Maybe Batman and Superman have a bit of a misunderstanding at first, with the Batfam trying to protect Gotham's interests while the League has a broader view.
In a 'justice league meets batfam fanfiction', there might be some interesting character interactions. For example, the Flash could be amazed by Robin's agility. Also, Wonder Woman might teach Batgirl some combat techniques. And there could be a lot of banter between the more light - hearted members of both groups, which would add some humor to the story.
I think Robin could be very interesting. He's young and full of energy, and in a meeting with the Justice League, he could be in awe of them at first but then prove himself. He might learn new skills from the League members and also show them that the Batfam has its own strengths. For example, his acrobatics and quick thinking could come in handy during a mission, and his interactions with characters like Aquaman or Green Lantern could be really fun to read about.
Spiderman himself could be the one to initiate an alliance. He's used to working with other heroes and he has a friendly personality. When he meets the Batfam, he would see the potential in working together and might reach out first. He would probably start with some light - hearted banter to break the ice and then suggest they team up to take on the bad guys in Gotham.
Definitely Batman and Wonder Woman. Their different outlooks on justice would create some intense conversations. Batman is more about the gritty, street - level justice, while Wonder Woman has a more idealistic, Amazonian view.