In one of the Travis Strikes Back scenarios, it's strongly implied that the antagonist of the next game might be an IT business tycoon that runs an urban revitalization company that have their sights set on Santa Destroy. They supposedly have a whole bunch of future tech on them, which might play into Suda's comments about Travis going up against some Thanos-level threats, and Santa Destroy is likely to see some kind of major overhaul because of that.
Travis manages to piss the guy off something fierce because he beat him to an inch of his life as vengeance for him having abused Juvenile (this game's "antagonist" and the creator of the video games you explore), so the antagonist of the next game is most likely going to be partially fueled by a personal vendetta. The guy in particular is a parody of soulless business execs, and his backstory is actually one giant parody of the way EA managed to creatively stifle Shadows of the Damned (right down to him having the same surname as John Riccitiello).
On the topic of that, NMH3 may feature Garcia Hotspur, but most likely not. He shows up after the fight against Eight Hearts and lets Travis know that if he needs help he'll repay him the favor, though Travis declines at the time.
It's also mentioned early in the story that Travis had a wife and kid that he left behind (possibly Sylvia and Jeane), but mentioned "that's another story", which doesn't get resolved in this game.
Whether Badman is going to be important is unknown, they succeed in resurrecting Bad Girl, but because they had an incomplete Death Ball, she gets resurrected as a Dog. Since the actual Bad Girl will be back for the second DLC, we'll have to see if it answers any questions about whether the two of them will be important.
Shinobu is most likely going to be important because she's the one who tracks down Travis to bring him out of hiding.