When each one reaches a certain level, you'll have the option to select which class you'd like them to promote to. While there was some reclassing in the previous titles, Fire Emblem Echoes requires a certain amount of free choice. Faye particularly seems to be a cause for confusion, so we've narrowed it down.
In the tweet below, we can see the images of Faye with a pegasus, indicating that pegasus knight is her canon class. If lore is important to you, this might be the right choice for you.
However, if you're interested in this choice from a strategic perspective, cleric seems to be the way to go. Faye gets abilities that no healer in Alm's group can get including "Again" which is like dancing/singing from previous games that allows other characters to make a second turn.
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