Brock of Pewter City

Type: Rock
Prizes: $1400, TM39 Rock Tomb, Availability to Flash
Suggested Pokemon: Mankey

Geodude @ None Level 12 Ability: Rock Head - Tackle - Defense Curl

Onix @ None Level 14 Ability: Rock Head - Tackle - Bind - Rock Tomb

Brock, being the first gym leader, is also the easiest. His team can be taken down by a Water-type or a Grass-type. Thing is... there aren't any of these available before him. Mankey, on the other hand, can put a hurting on Brock's team, despite Onix's excellent Defense. Your starter will also help, especially Squirtle and Bulbasaur, but Charmander gets access to Metal Claw at level 13, so there's no worries there.

Misty of Cerulean City

Type: Water
Prizes: $2100, TM03 Water Pulse, Availability to Cut
Suggested Pokemon: Paras, Pikachu

Staryu @ None Level 18 Ability: Natural Cure - Tackle - Recover - Harden - Water Pulse

Staryu @ None Level 21 Ability: Natural Cure - Rapid Spin - Swift - Recover - Water Pulse

Paras is a great candidate for Misty, as well as Pikachu. With availability to Bug AND Grass type moves, it's the perfect counter for Starmie. Stun Spore or Poisonpowder it, then spam Leech Life or switch into Pikachu to zap it.

Lt. Surge of Vermillion City

Type: Electric
Prizes: $2400, TM34 Shock Wave, Availability to Fly
Suggested Pokemon: Geodude

Voltorb @ None Level 21 Ability: Soundproof - Shock Wave - Tackle - Sonicboom - Screech

Pikachu @ None Level 18 Ability: Static - Quick Attack - Double Team - Thunder Wave - Shock Wave

Raichu @ None Level 24 Ability: Static - Quick Attack - Double Team - Thunder Wave - Shock Wave

Geodude shouldn't have much of an issue here, considering none of their attacks can really damage it much. It learns Magnitude at level 16, and that's all you're going to need to defeat Lt. Surge.

Erika of Celadon City

Type: Grass
Prizes: $2900, TM19 Giga Drain, Availability to Strength
Suggested Pokemon: Fearow, Pidgeotto, Vulpix/Growlithe

Victreebel @ None Level 29 Ability: Chlorophyll - Giga Drain - Stun Spore - Acid - Poisonpowder

Tangela @ None Level 24 Ability: Chlorophyll - Poisonpowder - Constrict - Ingrain - Giga Drain

Vileplume @ None Level 29 Ability: Chlorophyll - Sleep Powder - Acid - Stun Spore - Giga Drain

Erika's team isn't very defensive (besides Tangela) and can be taken down by any strong Flying-type, like Pidgeot and Fearow. Fly will take down just about every one of Erika's team. Vulpix and Growlithe will also deal with Erika well.

Koga of Fuschia City

Type: Poison
Prizes: $4300, TM06 Toxic, Availability to Surf
Suggested: Hypno, Kadabra

Koffing @ None Level 37 Ability: Levitate - Sludge - Smokescreen - Toxic - Selfdestruct

Koffing @ None Level 37 Ability: Levitate - Sludge - Smokescreen - Toxic - Selfdestruct

Muk @ None Level 38 - Minimize - Acid Armor - Toxic - Sludge

Weezing @ None Level 43 - Tackle - Sludge - Toxic - Smokescreen

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Koga's team is unbalanced, but his Pokemon are sturdy to non-supereffective attacks. Bring along a strong Psychic-type to take him down. Hypno works by hypnotizing them and using Dream Eater or can just attack head on with Psychic. Alakazam is even better, but Hypno is sturdier and easier to obtain.

Sabrina of Saffron City

Type: Psychic
Prizes: $4300, TM04 Calm Mind, Availability to Rock Smash
Suggested Pokemon: Haunter/Gengar

Kadabra @ None Level 38 - Psybeam - Reflect - Future Sight - Calm Mind

Mr. Mime @ None Level 38 - Psybeam - Barrier - Baton Pass - Calm Mind

Venomoth @ None Level 38 - Psybeam - Gust - Supersonic - Leech Life

Kadabra @ None Level 38 - Psychic - Recover - Future Sight - Calm Mind

Sabrina's pretty challenging, considering Psychic is a great offensive type. Ghost is your only hope of beating her, so use a Haunter or Gengar to smack her team around. Venomoth will need a Fire-type or Rock-type, but besides that, you shouldn't have much of a problem.

Blaine of Cinnabar Island

Type: Fire
Prizes: $4700, TM50 Overheat, Availability to Waterfall
Suggested Pokemon: Golduck, Gyarados

Growlithe @ None Level 42 Ability: Intimidate - Bite - Take Down - Roar - Fire Blast

Ponyta @ None Level 40 Ability: Flash Fire - Stomb - Bounce - Fire Spin - Fire Blast

Rapidash @ None Level 42 Ability: Flash Fire - Stomb - Bounce - Fire Spin - Fire Blast

Arcanine @ None Level 47 Ability: Intimidate - Bite - Take Down - Roar - Fire Blast

Blaine's team is basically the same two Pokemon just stronger. A Gyarados will take care of him completely, as well as a Golduck. Rain Dance sets are great as well, and dampen his Pokemon's ability.

Giovanni of Viridian City

Type: Ground
Prizes: $5000, TM26 Earthquake
Suggested Pokemon: Gyarados, Starmie

Rhyhorn @ None Level 45 Ability: Lightningrod - Take Down - Scary Face - Rock Blast - Earthquake

Dugtrio @ None Level 42 Ability: Sand Veil - Slash - Sand Tomb - Mud Slap - Earthquake

Nidoqueen @ None Level 44 Ability: Poison Point - Poison Sting - Body Slam - Double Kick - Earthquake

Nidoking @ None Level 45 Ability: Poison Point - Poison Sting - Thrash - Double Kick - Earthquake

Rhyhorn @ None Level 50 Ability: Lightningrod - Take Down - Scary Face - Rock Blast - Earthquake

Gyarados will be able to sufficiently take down Giovanni, though a special Water-type like Starmie will also work great, especially for Nidoking and Nidoqueen.