First off, I assume the Pokemon in this story will be characters in their own right, in which case I think you might be biting off more than you can chew by giving three or four Pokemon to each character, and six to the lead. It's worth noting that pretty much every main character in the Pokemon anime had about one Pokemon except for Ash, who had four or five. Team Rocket had one a piece, plus Meowth, and later on they pick up Wobbuffet, Misty had Psyduck and Staryu, the latter of which almost never appeared, Brock had...I can't even remember, he used them so rarely. I'm pretty sure a Geodude? Maybe an Onyx, too? He had an Onyx in the game.
Also, handing out guns to criminals is probably a poor idea in a Pokemon fic.
Edgar: Chlorine, I choose you!
BANG!
Edgar: ...Princess, I choose you!
BANG! BANG! BANG!
Edgar: Um...Scholar, I cho-
BANG!
I like the Team Rocket duo, though. Edgar and Jade seem like they could be interesting characters, but I'm wondering what story purposes they serve. Are they traveling together, is Jade a rival sort of character, or do they not interact much at all?
I understand what you mean and I considered that; however, I decided it would be a more deviant reflection on the evolution of Team Rocket after Giovani left and the organization split.
Firearms wont be in constant use in the story but it will reflect the Rockets combining conventional firepower with their pokemon; thats not to say it will always work (example, I've worked up one sequence where Sebastian attempts to use his firearm but Wright's Abra has put up a barrier between them and the battlefield, to which Sebastian ironically calls a cheap trick)
Though I wrote Edgar first, possibly giving the impression he is the main character, I would actually say he is a supporting character, somewhat a mentor and thinker. Jade would likely take the place as main character as he has room to grow and learn.
As for number of Pokemon; most of Wright's are not particularly battle trained (and most are characters in their own right, I'll post some bios later), most other pokemon I havent decided yet. Thats one area I'm working on, and I'm still trying to figure out some fitting pokemon for the characters.
The thing with characters is that no one can tell you if they'll be good or bad just by looking at a description. Your descriptions themselves are okay, but that's all they are: descriptions of a person. To get a decent feel of a character, I'd need to see them in story context. :)
For now, I'd just make sure you don't make too many characters, because sometimes following a massive cast can be pretty difficult. Unless your story was extremely long in length, chances are some of those characters wouldn't get quite as much character development when they should have, and thus they'd all wind up short something.
As for Pokémon, you gave give your characters as many as you want, just maybe focus on about one or two out of the whole team. That doesn't mean just skip on them entirely, I just mean it might be easier to get the reader more familiar with one or two Pokémon per person than it is a whole team.
I'm actually hoping this idea will have some length, though not as a single fic. Perhaps alot of fics put together; I've had some ideas already. Some focus around Team Rockets crimes (one idea is that the Rockets hijack a truck meant for the Celadon City Drugstore and Saffron City Police Dept.; The drugs (Carbos, Iron, ect.) and Pokemon food are laced with a Paralysis agent, and when the police force's pokemon are weakened, and other trained in chaos, Rocket squadrons would have a field day) along with some research based ones (I always wanted to tackle the Cubone-Kangaskhan Theory) and some more neutral ones (I've come up with a story where a foreign assistant sends a Banette to Wright to be studied, one of Wright's mail checkers, someone who disregards junk, doesn't recognize the pokemon and just figures it a doll, and gives it to his neice.)
I got a good few ideas, hopefully I can share a bit more and actually get them written.