Name: Brock
Gym: Pewter City Gym
Badge: Boulder Badge
Pokémon: Geodude L.12 , Onyx L.14
Element: Rock
Items Recieved: TM34 Bide
If you started with Squirtle or Bulbasaur, you should have an easy time of beating Brock. If you started with Charmander, you should probably pick up a grass pokémon on your way to Brock's gym. If your pokemon have higher levels than his, you should have no trouble beating him. Fire, ice, electric, poison, rock and flying types will have a hard time with him, but fighting, ground and grass will find it easy.
Name: Misty
Gym: Cerulean City Gym
Badge: Cascade Badge
Pokémon: Staryu L.18 , Starmie L.21
Element: Water
Items Recieved: TM11 Bubblebeam
If you started with Charmander, you will have a very hard time with Misty. You should use that strong grass type pokémon you used for Brock. Squirtle should be okay against her water types. Bulbasaur will find it really easy to beat the water type pokemon Misty has, so long as he uses grass/plant type attacks. Fire, ground, rock, fighting and poison types will have a hard time against Starmie, but water, electric, grass, dragon and psychic type pokémon can beat her easily.
Name: Lt. Surge
Gym: Vermilion City Gym
Badge: Thunder Badge
Pokémon: Voltorb L.21, Pikachu L.18, Raichu L.24
Use: Strong water, ground or rock
Element: Electric
Items Recieved: TM24 Thunderbolt
This time, Squirtle will be good against the electric type pokémon. Bulbasaur won't be that bad either. Charmander is okay, but whoever you use, make sure you have a lot of paralyze heals because of the electrifying attacks. Flying type pokémon will have a harder time because electric is strong against flying. Electric, grass and dragon types are the way to go.
Name: Erika
Gym: Celadon City Gym
Badge: Rainbow Badge
Pokémon: Victreebell L.29, Tangela L.24, Vileplume L.29
Element: Grass/Plant
Items Recieved: TM21 Mega Drain
Now, if you started with charmander, this gym will be a piece of cake. His fire attacks will blow away those grass types. Squirtle will find it harder, because his water attacks aren't strong against plants. Bulbasaur is okay, because he's against other pokémon of his type. Water, ground and rock pokémon will be hard pressed against these plant pokémon, but fire, grass, poison, bug, flying and dragon types are really good.
Name: Sabrina
Gym: Saffron City Gym
Badge: Marsh Badge
Pokémon: Kadabra L.38, Mr. Mime L.37, Venomoth L.38, Alakazam L.43
Element: Psychic
Items Recieved: TM46 Psywave
Just about the only good pokémon against psychic type is other psychic type! So long as you don't use fighting or poison types, you should do fine. Sabrina is almost the hardest leader to beat!
Name: Koga
Gym: Fuschia City Gym
Badge: Soul Badge
Pokémon: Koffing L.37, Muk L.39, Koffing L.37, Weezing L.43
Element: Poison
Items Recieved: TM06 Toxic
When you fight Koga, be sure to have lots of Antidotes handy, as his poison type pokémon will poison your pokémon! Other poison types, ground types, rock types or ghost types will be most effective against him. Don't use grass or bug types, but anything else with enough levels should be fine.
Name: Blaine
Gym: Cinnabar Island Gym
Badge: Volcano Badge
Pokémon: Growlithe L.42, Ponyta L.40, Rapidash L.42, Arcanine L.47
Element: Fire
Items Recieved: TM38 Fire Blast
If you started with Squirtle, he will be having the time of his life (as Blastoise, of course) beating up these fire pokémon. Fire, water, rock and dragon are the best types to use against these fiery pokémon. Grass, ice and bug are vulnerable to the fire attacks, so don't use them. Have lots of Burn Heals, just in case.
Name: Giovanni
Gym: Viridian City Gym
Badge: Earth Badge
Pokémon: Rhyhorn L.45, Dugtrio L.42, Nidoqueen L.43, Nidoking L.45, Rhydon L.50
Element: Ground
Items Recieved: TM27 Fissure
Grass and bug type pokémon will really come in handy against these ground types. Flying, fire, poison and rock types aren't very good, though. Once you beat Giovanni, you can go on to Victory Road and Indigo Plateau.