If you got one strong Pokemon in the 60's but the rest are in the 20's and 30's, you'll have to grind until your other 5 are on par with your Pidgeot. Else, it might be best to start over from scratch with a plan as to how you intend to beat not only the 8 Gym's but also assemble and train the best team to easily handle and defeat the Elite 4 and your rival(in this case Gary or whatever you opt to call him).
Before I start, may I ask what version of the game you happen to be playing because your strategy can differ depending on whether its Red/Blue or Yellow. However, the following strategy seems to work best:
Red/Blue: Your strategy over the course of the game is largely dependent on what starter you get. Most people prefer Charmander because even though he's weak/useless against the first 2 Gym's, he's viable for the next 5 Gym's and can defeat Lorelai's Pokemon with a nice Flamethrower(and his final form allows him to learn Fly, which can handle 3 of Bruno's Pokemon and one of Gary's final 6). If you go Bulbasaur, first 3-5 Gym's can be done with ease but afterwards will have a difficult time as type advantage goes away(although against the 8th Gym you have a slight edge, although I prefer Water when battling that one). Against Elite 4, Bulbasaur can cake walk over Lorelai provided you don't miss and get whacked by her Ice Attacks. Also can walk over Bruno's Rock Pokemon. If you opt for Squirtle, Brock is a breeze and even Misty can be beaten using Bite(although Bubblebeam still stings) but Gym's 3 and 4 are a mess and even 5-6 aren't ideal(but can be beaten). Final 2 are Squirtle's strong point though. Elite 4 wise, only Bruno and Lance(with Ice Beam/Blizzard) are trainers Squirtle has any real type advantage against.
Final 6 composition for Red/Blue:
Charmander(Fire Type): Starter. If not starter, swap for Vulpix(Celadon City) or another fire type. You will want one for Erika, Blaine(emergency backup), Koga(just watch for Poison) and Sabrina(Slash and Flamethrower do decent damage). Elite 4 wise he's kind of useless except against Bruno Fighting Types using Fly. I would consider using him against Lorelai but Grass/Electric are better options in my opinion.
Squirtle(Water Type): Starter. If not starter, Lapras, Cloyster or another Water Type that learns Ice Type moves(like Vaporeon or Dewgong) is recommended. Strong against Brock, Blaine, Giovanni, Bruno, Lance(Ice Type moves) and final battle.
Bulbasaur(Grass Type): Starter. If not starter, recommend Victrebell/Vileplume as its replacement. Strong against Brock, Misty, Lt.Surge, Koga(due to being Poison Type as well), Lorelai, Bruno and final battle.
Pidgey/Spearow(Flying Type): Catch it relatively early and a strong counter to Fighting, Grass and Bug Types. Only really useful against Misty, Erika, Sabrina, Fighting Dojo and Bruno's Fighting Pokemon. Doduo is another strong alternative. If you have Charizard that knows Fly, can swap for a different Pokemon.
Pikachu(Electric Type): Can be found in Viridian Forest and is an optimal Pokemon for Misty, Lorelai, Lance's Gyrados and any Flying/Water Types in Final Battle. Optionally Jolteon is a solid choice.
Sandshrew/Geodude(Ground Types): Can be found relatively early and is a solid choice for Lt.Surge, Erika(Ground moves hurt her Grass/Poison types), Koga(Ground KO's Poison), Blaine and particularly Agatha(Ghost's are part Poison).
*Flex: If you have Charmander, then it evolves into Charizard(from which you can teach it Fly). If that is the case, then you can sub in whatever you want into the Pidgey/Spearow slot. Can be a Psychic type, Dragon type(Dragonite being the only option) or some Bug/Normal Type that you wanted to have tag along.
Yellow: Yellow is different from Red/Blue in that your starter is always Pikachu. Furthermore, you gain all 3 Kanto starters for free, which makes building your team that much easier. Each Kanto Starter is honestly worthwhile to have, although if you opt to replace one, then the options I noted for Red/Blue are recommended. However, you don't get any of the Kanto starters until Cerulean so you have to counter Brock with either a Mankey, Nidoran or Butterfree. End Game composition is as follows:
Pikachu(Starter): Solid option and one of your strongest being a starter. Don't have to repeat what its strong against do I?
Charmander(Fire Type): Obtained for free in Cerulean and evolves into Charizard that can learn Fly. Big help against Koga who has 3 Venonats and a Venomoth in Yellow version and can own Erika in no time flat. Also is surprisingly strong against Sabrina, and Bruno's Fighting Pokemon. Lorelai's Jynx is the only one I'd consider utilizing him against. Rest can be KO'd with Grass/Electric moves.
Bulbasaur(Grass Type): Obtained for free in Cerulean(can even be acquired before Misty) that is a solid option throughout the game. Misty(LMK if you want to know how to acquire it before Misty), Lt.Surge, Erika(same type but watch for Stun Spore/Sleep Powder), Lorelai and Bruno's Rock Pokemon are at the mercy of Bulbasaur.
Squirtle(Water Type): Obtained for free in Vermilion and can handle most opponents. Doesn't shine until Blaine/Giovanni though but Ice attacks against Koga are viable option, as is battling Sabrina with strong Water abilities. Also owns Bruno's Rock Pokemon and Lance's Dragons with Ice Attacks.
Sandshrew(Ground Type): Obtained relatively quickly(prior to Mt.Moon) that once it learns Dig can handle Lt.Surge, Erika, Koga(first 3 Venonats, Dig useless against Venomoth), Sabrina, Blaine and notably Agatha. Geodude or another Ground Type with Ground Type moves are optional.
*Flex* With Charizard in your team, you pretty much don't need anything but the above five to beat the snot out of everyone. I typically put a Psychic Type like Kadabra, Drowzee or Mew(yes the special case of Ditto Glitch can be done early) in this slot as a backup for Agatha and any situation that calls for it. Right now though, I have Dragonite because well... I can.
Any questions or issues, feel free to ask.
