Cinnabar Gym
Leader Blaine: Growlithe (Lv42), Ponyta (Lv40), Rapidash (Lv42), Arcanine (Lv47)
Good pokemon to use: Any water pokemon with Surf (Blastoise, Vaporeon, Starmie, Lapras); any ground pokemon with Earthquake (Dugtrio @ Lv51, Graveler/Golem @ Lv45, Sandslash, Nidoking, Marowak with TM 26). Have team around Lv44.
Viridian Gym
Leader Giovanni: Rhyhorn (Lv45), Dugtrio (Lv42), Nidoqueen (Lv 44), Nidoking (Lv45), Rhyhorn (Lv50)
Good pokemon to use: Any water pokemon with Surf; any Grass pokemon with a strong grass move for Rhyhorn/Dugtrio (Venusaur with Razor Leaf @ Lv22 or Solarbeam @ Lv65); any pokemon with Earthquake for Nidoqueen/king. Have team around Lv47.
Elite Four
Lorelei
Lv52 Dewgong
Lv51 Cloyster
Lv52 Slowbro
Lv54 Jynx
Lv54 Lapras
Bruno
Lv51 Onix
Lv53 Hitmonchan
Lv53 Hitmonlee
Lv54 Onix
Lv56 Machamp
Agatha
Lv54 Gengar
Lv54 Golbat
Lv53 Haunter
Lv56 Arbok
Lv58 Gengar
Lance
Lv56 Gyarados
Lv54 Dragonair
Lv54 Dragonair
Lv58 Aerodactyl
Lv60 Dragonite
Rival
Lv59 Pidgeot
Lv57 Alakazam
Lv59 Rhydon
Lv59 Gyarados / Exeggutor / Arcanine
Lv61 Arcanine / Gyarados / Exeggutor
Lv63 Venusaur / Charizard / Blastoise
By the Elite Four, you should have your team settled out. Just be around level 55+, and if lower, be sure to stock up on Hyper Potion, Revive, Full Restore. If you're low on money, buy Lemonade in Celadon's mall or earn money with the Amulet Coin attached (given by an aide on Route 16). Any team can beat in-game pokemon, so just keep raising your team and you'll prevail. Good luck.
I suggest using your starter, Starmie, Aerodactyl, Jolteon, Gengar, Alakazam, Mewtwo, Dragonite, Gyarados, Raichu, Vaporeon, Pidgeot, etc.