As long as you meet the prerequisite, pick any class
These are separate things. As you note, the requirement is just "Intelligence or Wisdom 13 or higher". This means you need either "Intelligence 13 or higher" or "Wisdom 13 or higher". If you have an Intelligence of 1 but 13 Wisdom you still qualify for the feat.
Once you qualify for the feat, the choice of class is not tied to the requirements or your stats in any way (any such limitation would have to be stated in the feat). The picked class only determines the possible spells and the spellcasting ability used. If you pick wizard you will always use Intelligence regardless of the Ability Score you used to qualify for the feat.
It might seem at first that the Ability score requirements were tied to the spellcasting abilities of the chosen classes but also note that "Charisma 13 of higher" is not included in the prerequisites even though you can pick bard, sorcerer or warlock which use Charisma, further suggesting that there is no implicit link between the stat and the spell list.1
1. Noted by NathanS