Pidgeot is a Normal-Flying type, and as such, it is weak to Rock, Electric, and Ice moves. (It will take double damage from these types of attack). A Pokemon that is one of those types would make those moves even stronger, so a Rock, Ice, or Electric type Pokemon with a signature same-type move should be the best against it.
Pidgeot is immune to Ground and Ghost moves, and resistant to Bug and Grass. It will take normal damage from Normal, Flying, Fighting, Poison, Steel, Fire, Water, Psychic, Dark, Fairy, and Dragon moves.
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It depends who you chose. If you chose Squirtle he will have Venusaur, Arcanine, Gyarados, Rhydon, Pidgeot and Alakazam. If you chose Bulbasaur he will have Charizard, Rhydon, Pidgeot, Alakazam, Exeggutor and Gyarados. And if you chose Charmander he will have Blastoise, Pidgeot, Arcanine, Exeggutor, Alakazam and Rhydon. So you will need a water type for Arcanine, Charizard and Rhydon. An Ice type for Pidgeot, a dark type for Alakazam and Exeggutor, an electric type for Gyarados and Blastoise, and a fire type for Venasaur, so the best team would be Raichu, Haunter, your starter, Alakazam, Onix and Pidgeot.
Ground type Pokemon can beat Electric type Pokemon easily.
in Pokemon crystal the best Pokemon to have are feraligator(evolved form of totodile), weepinbell, kadabra, ledian (i would advise you to this Pokemon ice punch and headbutt), and pidgeot. these are the Pokemon i beat the elite four with
Dark type can beat ghost.
Rock, electric and ice.