This team will be valid no matter the starter. This is for Pokemon Crystal so if youre playing Gold or Silver some things may not be possible for you. Im listing HMs to the movesets so make sure yourself that you only give one of each of those to your Pokemon.
1 FIRE TYPE
Typhlosion: Flamethrower/Fire Blast, Thunder Punch, Strength/Headbutt/Cut, Dynamic Punch
Arcanine: Flamethrower/Fire Blast, Return, Rest, Sleep Talk
2 WATER TYPE
Feraligatr: Surf, Whirlpool/Ice Punch, Dynamic Punch, Cut/Strength/Headbutt
Gyarados: Surf, Waterfall/Whirlpool, Thrash/Strength, Zap Cannon
3 GRASS TYPE
Meganium: Cut/Strength/Headbutt, Synthesis, Razor Leaf/Giga Drain, Light Screen/Reflect
Victreebel: Cut/Return, Razor Leaf/Giga Drain, Sludge Bomb, Sleep Powder
4 EGG POKEMON
Whatever Pokemon you got from the odd egg.
Wigglytuff: Strength/Double-Edge/Body Slam, Ice Beam, Thunderbolt/Thunder, Sing/Sweet Kiss
Clefable: Strength/Return, Moonlight, Ice Beam, Thunderbolt/Thunder
Electabuzz: Strength/Fire Punch, Thunderbolt, Ice Punch, Dynamic Punch/Light Screen
Jynx: Ice Beam, Sweet Kiss, Psychic, Perish Song
Raichu: Thunderbolt, Thunder Wave, Dynamic Punch/Iron Tail, Strength/Return
Im not listing Magmar since you already have Arcanine/Typhlosion as a fire type and I'm not listing Tyrogues evolutions either since later in this list therell be better options for a fighting type. If you got either of those two and not one of the other five (or you did get one of the other five but you just dont want to use the one you got) you could use one of these:
Espeon: Psychic, Morning Sun, Protect, Toxic
Jolteon: Thunderbolt/Thunder, Baton Pass, Agility, Thunder Wave
5 - FLYER
Dragonite: Fly, Whirlpool/Waterfall, Thunderbolt/Thunder/Dynamic Punch, Ice Beam/Outrage/Thunder Wave/Extreme Speed
Since you get Dragonite pretty late before getting him you could use Fearow, Pidgeot or any other flying type you want before getting him.
6 - EXTRA
You can use pretty much anything you want. I definitely recommend Heracross.
Heracross: Endure, Reversal, Megahorn, Earthquake
Here are some other options though if you dont want him:
Pinsir: Strength/Return, Seismic Toss, Submission, Swords Dance
Scyther: False Swipe, Swords Dance, Steel Wing, Return/Slash
Graveler: Earthquake, Rollout, Explosion, Strength/Rock Throw/Headbutt
Machoke: Earthquake, Cross Chop, Seismic Toss, Strength/Return/Curse