Here, I will put the Gym Leaders pokémon, their corresponding badges, and their home turf. I will also recommend a pokémon and a type against each Gym Leader. The pokémon I recommend is part of the pokémon you could've gotten by now. Again, avoid the extra words at the bottom of the page. The HTML is screwed up.

Pewter City
Brock uses rock-type pokémon.
Geodude: Level 12
Onix: Level 14
I recommend a water-type pokémon: Squirtle.
Do not use a fire or electric-type pokémon here: Charmander and Pikachu.

Cerulean City
Misty uses water-type Pokémon.
Staryu: Level 18
Starmie: Level 21
I recommend a grass or electric-type pokémon here: Bulasaur/Ivysaur and Pikachu.
Do not use a rock-type pokémon against Misty: Geodude.

Vermilion City
Lt. Surge uses electric-type pokémon.
Voltorb: Level 21
Pikachu: Level 18
Raichu: Level 24
I recommend a ground-type pokémon for this battle: Geodude.
Do not use a water, flying or electric-type pokémon against this Gym Leader: Squirtle/Wartortle, Pidgey/Pidgeotto or Pikachu.

Celadon City
Erika uses plant-type pokémon.
Victreebell: Level 29
Tangela: Level 24
Vileplume: Level 29
I recommend a fire, poison, flying, or bug-type pokémon :Charmander/Charmeleon, Pidgey/Pidgeotto, Spearow/Fearow, Weedle/Kakuna/Beedrill.
Do not use a water, electric, grass or ground-type pokémon here: Squirtle/Wartortle, Pikachu/Raichu, Bulbasaur/Ivysaur or Geodude/Graveler.

Saffron City
Sabrina uses psychic-type pokémon.
Kadabra: Level 38
Mr.Mime: Level 37
Venomoth: Level 38
Alakazam: Level 43
I recommend a bug-type pokémon versus her: Paras/Parasect, Weedle/Kakuna/Beedrill or Caterpie/Metapod/Butterfree.
Do not use a fighting or a psychic type pokémon in this fight: Machop/Machoke, Hitmonlee, Hitmonchan, Mankey/Primeape, Abra/Kadabra.

Fuchsia City
Koga uses poison-type pokémon.
Koffing: Level 37
Muk: Level 39
Koffing: Level 37
Weezing: Level 43
I recommend a ground or psychic-type pokémon against Koga: Geodude/Graveler, Onix, Abra/Kadabra.
Do not use an electric, fighting or poison-type pokémon here: Pikachu/Raichu, Voltorb/Electrode, Hitmonlee, Hitmonchan, Machop/Machoke, Mankey/Primeape.

Cinnabar Island
Blaine uses fire-type pokémon Growlithe: Level 42
Ponyta: Level 40
Rapidash: Level 42
Arcanine: Level 47
I recommend a water, ground or rock-type pokémon against fire: Squirtle/Wartortle/Blastoise, Geodude/Graveler.
Do not use fire, electric, grass or bug-type pokémon:Charmander/Charmeleon/Charizard, Pikachu/Raichu, Voltorb/Electrode, Bulbasaur/Ivysaur/Venusaur, Paras/Parasect, Caterpie/Metapod/Butterfree, Weedle/Kakuna/Beedrill.

Giovanni uses Ground and Rock-type pokémon.
Rhyhorn: Level 45
Dugtrio: Level 42
Nidoqueen: Level 43
Nidoking: Level 45
Rhydon: Level 50
I recommend a water, grass or ice-type. At least one of those types should be on your team:Squirtle/Wartortle/Blastoise, Bulbasaur/Ivysaur/Venusaur, Lapras, Jynx.
Do not use an electric, poison or rock-type pokémon in the battle for the EARTHBADGE: Pikachu/Raichu, Voltorb/Electrode, Electabuzz, Magnemite/Magneton, Koffing/Weezing, Grimer/Muk, Geodude/Graveler.

The Elite Four

Lorelei uses water and ice-type pokémon.
Dewgong: Level 54
Cloyster: Level 53
Slowbro: Level 54
Jynx: Level 56
Lapras: Level 56
I recommend a grass-type pokémon when fighting against her: Bulbasaur/Ivysaur/Venusaur is probably your bast bet.
Do not use a rock, ground, fire-type pokémon:Geodude/Graveler, Charmander/Charmeleon/Charizard.

Bruno uses fighting and rock/ground-type pokémon
Onix: Level 53
Hitmonchan: Level 55
Hitmonlee: Level 55
Onix: Level 56
Machamp: Level 58
I recommend a flying or psychic-type pokémon here: Articuno, Zapdos, Moltres, Pidgey/Pidgeotto/Pidgeot, Abra/Kadabra.
Do not use bug or rock-type pokémon in this battle: Caterpie/Metapod/Butterfree, Weedle/Kakuna/Beedrill, Geodude/Graveler, Onix.

Agatha uses ghost-type pokémon
Gengar: Level 56
Golbat: Level 56
Haunter: Level 55
Arbok: Level 58
Gengar: Level 60
I recommend a Geodude/Graveler and its attack EARTHQUAKE.
Do not use a fighting-type pokémon against Agatha: Machop/Machoke, Mankey/Primeape, Hitmonlee, Hitmonchan.

Lance uses dragon-type pokémon
Gyarados: Level 58
Dragonair: Level 56
Dragonair: Level 56
Aerodactyl: Level 60
Dragonite: Level 62
I recommend a ice or dragon-type pokémon here: Jynx, Lapras, Dratini/Dragonair/Dragonite.
Do not use a fire, water, electric or grass-type pokémon to defeat Lance: Charmander/Charmeleon/Charizard, Squirtle/Wartortle/Blastoise, Pikachu/Raichu, Bulbasaur/Ivysaur/Venusaur.

Gary uses a variety of pokémon.
Pidgeot: Level 61
Alakazam: Level 59
Rhydon: Level 61
Now, depending on which pokémon he chose at the beginning, his the second half of his team is different.

Bulbasaur

Gyarados: Level 61
Arcanine: Level 63
Venusaur: Level 65

Charmander

Exeggutor: Level 61
Gyarados: Level 63
Charizard: Level 65

Squirtle

Arcanine: Level 61
Exeggutor: Level 63
Blastoise: Level 65

It's up to you to choose which pokémon to use against the Elite Four and Gary. I can't recommend any pokémon for your battle against Gary. Create your team wisely...