I haven't seen an idea this great in a long time!
NORMAL:
Chansey - I've mentioned her name in a bunch of other threads, and I really want her added! First of all, she's a well-known Pokemon and she's been helping Nurse Joy for years. Secondly, Chansey would have a very unique play-style; a ton of health, minimal defense, and a lot of moves capable of healing. Unlike the other characters, Chansey could be unique in the sense that her goal is to stall out her opponents! Her counter attack, Protect, wouldn't deal any damage, but would completely shut down anything it touches; egg-throwing could make for interesting projectiles; and what's Chansey without Soft-Boiled? {XD}
Regigigas - In my opinion, Legends are the best, and if you're going to add one of the Regis into the game, why not the king of them all? They even have a stage with a giant Regigigas statue! With his Slow Start ability, Regigigas would make an interesting addition to the roster. All of his attacks would have HEAPS of end-lag, but deal obscene amounts of damage. I don't have too many ideas for Regigigas' attacks, but he could definitely utilize his long arms for ranged combat.
ROCK:
Tyranitar - He's amongst my six favorite Pokemon, so I HAD to put Tyranitar on my list. His tail would be his most powerful weapon; it could trip opponents to lead into combos, knock people into the air, and - overall - wreak a lot of havoc! Not only does he have plenty of physical attacks, he has a good amount of special attacks, such as Dark Pulse and Fire Blast! For Tyranitar's Burst Attack, he would Mega Evolve and use his 'signature' Stone Edge attack! What Tyranitar set doesn't run Stone Edge? :p
Kabutops - One of the less popular Pokemon, Kabutops would be an interesting choice since he represents fossils. With those long claws and small body, Kabutops would be capable of performing lengthy combos that deal large amounts of damage. I envision a lot of his attacks being multi-hitters, utilizing moves such as Fury Swipe and Rock Blast. Kabtuops would have good mobility, and seem like a cross between Weavile and Machamp.
BUG:
Pinsir - This guy has the perfect, humanoid shape for being in a game like Pokken Tournament. His Bug Buzz attack could interrupt an opponent's counter attack, but it wouldn't be a throw. U-Turn would be so much fun to use; initiating the attack causes Pinsir to run up to the opponent, attack with his horns, and then retreat! Another neat attack would be Infestation, which could hold your opponent still and slowly deal damage. The possibilities for Pinsir are endless!
Beedrill - Beedrill would hover just above the stage; he'd only rest his feet on it while crouching in Duel Phase. I think he would make a great aerial attacker, what with the ability to fly around. His stingers could unleash quick, poison-inducing attacks and set up excellent aerial combos. I envision Beedrill being a much faster, combo-heavy version of Charizard!
Scizor - The instant Pokken Tournament released, I was awaiting Scizor to be added as DLC... He would fall into the 'Standard' category, and could have a perfect balance of speedy lag-less moves, as well as heavier moves. X-Scissor, Headbutt, and Metal Claw would all deal a lot of damage, whereas Bullet Punch, Cut, and Struggle Bug would all come in quickly to finish the foe off.