Bug Type
Good against Grass, Psychic, Dark
Dark Type
Good against: Ghost, Psychic
Dragon Type
Good against: Dragon
Electric Type
Good against: Water, Flying
Fairy Type
Good against: Poison, Steel
Fighting Type
Good against: Normal, Ice, Rock, Dark, Steel
Fire Type
Good against: Grass, Ice, Bug, Steel
Flying Type
Good against: Grass, Fighting, Bug
Ghost Type
Good against: Ghost, Psychic
Grass Type
Good against: Water, Ground, Rock
Ground Type
Good against: Fire, Poison, Electric, Rock, Steel
Ice Type
Good against: Grass, Ground, Flying, Dragon
Normal Type
Does neutral damage to all type expect Ghost
Poison Type
Good against: Grass, Fairy
Psychic Type
Good against: Fighting, Poison
Rock Type
Good against: Ice, Fire, Flying, Bug
Steel Type
Good against: Ice, Rock, Fairy
Water Type
Good against: Fire, Ground, Rock
Fighting and Ground types cover the most types at 5 so I would definitely use a Fighting and Ground type move if you want a Pokémon that can hit the most types as the only type that Fighting and Ground type moves have in common against is Steel.
Fire, Ice and Rock type is next as it covers 4 different types. Fire type moves cover Grass, Ice, Bug and Steel types but Blastoise can't learn a Fire type move other than Hidden Power Fire and you are already covering Ice with Fighting and Steel with Ground so I wouldn't recommend it.
Ice type moves cover Dragon, Flying, Grass and Ground. I would definitely recommend an Ice type move if you were to also have a Fighting and Ground move as Ice covers completely different types that Fighting and Ground cover.
Rock types cover Flying, Fire, Bug and Ice but it is not recommended having as you are already covering Fire and Ice and Flying.
So far the type of moves I would recommend having for Blastoise:
A Fighting type move such as Focus Blast, Aura Sphere or Brick Break
A Ground type move such as Earthquake, Bulldoze or Hidden Power Ground
A Ice type move such as Ice Beam, Blizzard or Hidden Power Ice
And another move either a Dark type move such as Dark Pulse or Bite to hit Ghost and Psychic types or a Normal type move such as Skull Bash, Facade or Strength for neutral damage against all types expect Ghost
*Note having a Ground and an Ice type move covers both of your weaknesses as Ground covers Electric and Ice covers Grass.