There's not much of a point in not using your starter, it's a very solid Pokemon. With that said, there are a few Pokemon of each type that function quite well.
Grass
Tsareena @ anything
Ability: Queenly Majesty
EVs don't matter. Try 252 Spe / 252 Atk / 4 HP
Nature doesn't matter. Jolly is good.
- Power Whip
- Zen Headbutt
- Play Rough
- High Jump Kick
Roserade @ anything
Ability: Poison Point
EVs don't matter. 252 Spe / 252 SpA / 4 HP
Nature doesn't matter. Use Timid if you must.
- Energy Ball
- Dazzling Gleam
- Sludge Bomb
- Shadow Ball
Leafeon @ anything
Ability: Leaf Guard
EVs don't matter. 252 Atk / 252 Spe / 4 HP
Nature doesn't matter, but Jolly is good.
- Leaf Blade
- X-Scissor
- Quick Attack
- Swords Dance
Fire
Arcanine @ anything
Ability: Intimidate
EVs don't matter. 252 Atk / 252 Spe / 4 HP
Nature doesn't matter. Use Jolly
- Flare Blitz
- Crunch
- Wild Charge
- Play Rough
Volcarona @ anything
Ability: Flame Body
EVs: 252 SpA / 252 Spe / 4 HP
Timid Nature
- Psychic
- Flamethrower
- Bug Buzz
- Giga Drain
Centiskorch @ anything
Ability: White Smoke
EVs: 252 Atk / 252 Spe / 4 HP
Jolly Nature
- Fire Lash
- Leech Life
- Crunch
- Thunder Fang / Coil
Water
Barraskewda @ anything
Ability: Swift Swim
EVs: 252 Atk / 252 Spe / 4 HP
Jolly Nature
- Liquidation
- Throat Chop
- Drill Run
- Poison Jab
Gyarados @ anything
Ability: Intimidate
EVs: 252 Atk / 252 Spe / 4 HP
Jolly Nature
- Waterfall
- Earthquake
- Power Whip
- Stone Edge
Lapras @ anything
Ability: Water Absorb
EVs: 252 SpA / 252 Spe / 4 HP
Timid Nature
- Sparkling Aria / Surf
- Ice Beam
- Thunderbolt
- Psychic
Again, there isn't much point in not using your starter, but these are some solid choices if you don't.
Hope I helped!