I like both of the Tyrogue evolves that were in RBY. Not a big fan of Hitmontop.
Update: Beat Elite 4. Hardest they've ever been for me.
Obviously the psychic types were a big problem, I had to rely on beating their second type to stand a chance. (And Heracross' fury cutter after the pesky Xatu's were out the way).
Koga was equally annoying, especially his crobat and its flying moves.
After I finally got past Koga it was a walk in the park, beating my fellow fighting types in Bruno's team easily (where possible I made it his v. mine of the same pokemon, I OHKO'd all his).
Then the dark pokemon were easy, even the ones that weren't dark I just took down with Poliwhirl's surf.
Mega Punch took care of Gyarados, then Poliwhirl cleaned up the rest with Surf and Icy Wind.
Beat Blue eventually, though it seemed like his team was prepared specially to beat me, whatever he sent out seemed to just cause me more trouble, but I beat him finally. Alakazam almost OHKO'd all my pokemon, and I had to sacrifice Heracross (using take down) to win.
Red is tough. His Espeon can OHKO everything with psychic, meaning I need to wear down his PP with revives to stand a chance. D=
Charizards Wing Attack also OHKO's everything.
Man, fighting pokemon have it tough.
Edit:
Ok, done with the Fighting challenge, went in there planning to bide my time until Poliwrath's Quick Claw kicked in, due to Charizard OHKO'ing everything last time, and having the speed advantage. That didnt happen, because he decided to use Fire Spin against Poliwrath, which missed, Surf took over half its HP, then Poliwrath managed to Survive a Wing attack. Machamp and Hitmonlee took out Snorlax. Easy.
Blastoise was no problem either, Poliwrath put him to sleep and then Machamp Cross-Chopped away at his health. Venasaur was not much of a problem either, except that it survived long enough to wear down Heracross' HP due to Espeons Reflect.
But long story short, I finally won with my fighting pokemon, despite the type/level disadvantages I had against Red, and the awful typing in the Elite 4.
Fighting was a good Challenge, but I definitely used too many pokemon in my team, especially considering 3 of them were Pure-fighting type.
Next challenge...could you randomise it again? I like not knowing what I'm doing until I start ^^.