Hello user Ben Cousins.
Hearthome's leader, Fantina uses Ghost Type Pokemon, Duskull, Haunter and Mismagius, to be exact.
Gastly and Rotom are two ghosts types that you can use to hit Fantina with supereffective STAB attacks and are also very handy later in the game. Both can be caught in the Old Chateau, although Rotom must be caught at night, you encounter it by interacting with the TV in the room located on the second floor of the Old Chateau. In addition to this, if you have an action replay, you can get the Secret Key, which lets you enter the Room in the Galactic Eterna Building that allows your Rotom to change into a Rotom-A forme. Rotom-A has 50/107/107 Defenses and a Special Attack Stat of 105, so it essentially is better than Rotom and still retains the extremely reliable typing of Electric/Ghost.
Zubat and Shinx are also Pokemon that are found all around Sinnoh and can beat Fantina with Bite, Luxray and Crobat also serve ample purposes later in the game and help against many of the other Gym Leaders/Elite Four.
In addition to this, Houndoom, Roserade, Gastrodon, Garchomp, Lucario and Mamoswine are all great Pokemon that can greatly assist you in your campaign to beat the game.