Okay.. Why don't you just look this up yourself?
I'm going to do the FR/LG Pokemon League instead of the original due to it being more easily accessed, and them using I'm pretty sure, The same pokemon.
Lorelei - 4 of her 5 pokemon Go out with Electric, So this is a Definite Type to carry for her, and Anything Physical Takes out Jynx.
So, One Electric Type Move with Decent PP for this Battle.
Bruno - We're in a Generation where Psychic is Always Special.
All of his Fighting Types are weak to Psychic, and both of his Onix's Have Horrible Special Defense, but beastly Physical Defense, but for the Most part, You can just use a Strong Psychic move for this Guy's whole team.
Bertha - Everything in her Team Is Weak to Psychic, So Aslong as you are high enough over Gengar and Crobat to outspeed everything, Psychic Takes this battle Down.
Lance - Remember your Electric type from Lorelei? Pull him back out.
Gyrados and Aerodactly Go down with Electric Easy, Now a Simple Ice Beam takes out the Rest.
Gary - He has a well balanced team that you just need to hit with your Best Shot.
Kanto League's main Weakness - Its weakest to Psychic which takes down Bruno and Bertha, 2nd Weakness is Electric That takes down 4 of Lorelei and 2 of Lance. You can Carry a Starmie who knows,
Ice Beam( Lance ) - Thunderbolt ( Lorelei + Lance ) - Psychic ( Bruno + Bertha ) and Surf ( STAB for Rival )
And pretty much demolish the Pokemon League if you're slightly over Leveled.
Will - immediatly Goes down With Dark, ALL of his pokemon are weak to it, So just carry a Strong and hard hitting Dark Move.
Koga It says Poison, but he likes bugs Too.
Fire takes all of his Bugs Down, Not Pull out a Hard hitting Psychic type to Take Out Muk and Crobat.
You basically need Fire and Psychic.
Bruno - You just need Psychic for his whole battle again, Just need Psychic.
Karen - Psychic Takes down Gengar and Vileplume, Rock For Houndoom and Murkrow, and Hit Umbreon with Fighting,
My Suggestion would be a Fighting Type with a Rock move on it, And your Psychic type from Koga and Bruno.
Lance - Everyone in his team has a Rock Weakness, So this is a Definite, Since you already Get good use of it from Karen.
Johto League biggest disadvantages - I Think the best type with the most effectiveness and essentialness in this Pokemon League, Is Psychic, And the second most use Full being Rock.
No Hoenn Remakes :'(
Sidney - All of His Pokemon go down with Fighting In R/S or E.
Phoebe - Dark takes out everyone but Sableye, and with Sableye having no Weaknesses, Just hit him with the Strongest STAB move you can whip up.
Glacia - Her Whole Team goes down With Fighting.
Drake - In R/S His whole team is taken down with Ice, Although in Emerald He has a Kingdra who you just Have to hit with Strong STAB or a Dragon Move.
Champion Steven - Water hits everyone in his Team for Neutral or Super Effective, Same with Fire so This is the most beneficial types to use on him, Perhaps your Starter?
Champion Wallace - If you're playing emerald you face him instead of Steven here.
Electric Takes everyone but Whiscash, He needs a Grass move to be taken Down, While Ludicolo is Neutral on both but will go down with a Strong STAB move.
Biggest Type Threat - I think Fighting, Being able to take down the Dark and Ice Team Elite four Trainer, is the most needed type for this league.
I'm doing D/P not Platinum here.
Aaron - Hit him with Fire to take down 4 of 5 of his Guys, and Drapion goes down With Ground, or Strong STAB.
Bertha - All of her pokemon are weak to Grass.
Flint - Water Takes Down His Fire types ( 2 ) And his Steelix. Ice Takes Drifblim ( Most water types can get a hold of it ) And Lopunny goes down with Any Decent STAB Move.
Lucian - Only 3 of 5 have a Dark weakness, but that helps, and Fire It super Effective on Bronzong, and can Probably Take Medicham if its STAB.
Cyntha - Has a Rather Well balanced team, hit her with all you've got.
Type Threat - I'd Say fire does the biggest Damage here, Although in Platinum Ice Works best.
Finally, I'm almost done, I'm doing to before Elite Four pokemon League.
Shauntal - Goes down with Dark
Grimsley - Goes down with Fighting
Caitlin - Goes down with Dark
Marshal - Goes down with Psychic
Weakness - Dark is the biggest Weakness of this pokemon League, Even though I'm doing the before you battle N and Ghetisis Pokemon League, These are still base weaknesses that will take out a large amount of pokemon Afterwards, Biggest Threat is Dark Taking Down Caitlin and Shauntal