in the interest of rounding out the Pokémon headcanons… team gai Pokémon teams?? (aside from the tyrogue trio you mentioned before which is a great idea btw)

I think all of them have mostly Fighting types–given their jounin sensei is the master of taijutsu, and they themselves specialize in taijutsu–but each of them differ in their second types.

So Lee is mostly Fighting with some Normal (HARD WORK BEATS TYPE SPECIALIZING), Neji has Fighting and Psychic (which explains why he consistently beats Lee even though Lee is faster than god), and TenTen has Fighting and Steel.

As previously mentioned, all of them did get a Tyrogue from Gai (and each of them have a different evolved form). So while I’m not entirely sure what order each of them get these Pokemon, these are what I have in mind.