Jobs won't be getting mounts, only classes.
As for what I've seen in the past Live Letters and from what Artworks I've found.
Lancer will get a Drake mount.
Arcanist will get Fenrir mount.
As for Gladiator, Thaumaturge, Marauder, and Pugilist.. I'm not sure on that yet, haven't found many convincing screenshots or artworks done by the team at SE to make me lean towards them having mounts just yet.

There will however be job barding for chocobos.