The experts are united by expertise, and the priests by channel. I suspect the mages will be next, because all they need is for some mechanism to let them cast more spells than clerics, druids, and bards. That isn't too hard, which is why I think mages will be the next playtest.
The warriors have it a little harder, because traditionally anything that makes you better at hitting someone with a weapon ends up being available to all the melee classes. I don't see much that would make sense for a fighter, barbarian, and monk but not for a ranger or paladin to have.
Experts: Expertise
Priests: Channel Divinity/Nature
Warriors: Advanced Fighting Styles
Mages: Arcane Recovery
Is my guess. Warriors are next because they need the most work.