Clibinarii, Comitatenses First Cohorts, Scholae Palatinae or Auxilia Palatina, or their awe-inspiring siege weaponry.
The Romans do have some heavy hitters, infantry and cavalry alike, but they are constantly struggling against so many enemies, inside and outside their borders, you might want to think twice about playing them just so you can field Equites Catafractarii, E. Also, in the campaign, they have this opportunity to build up an empire from pretty much nothing. Personally, I like these best, with the Vandals as my favorite, a good base of infantry for defense and absolutly devastating cavalry for offense.
The desert and nomadic factions require a little more finesse, being cavalry heavy with a focus on horse archers. with infantry, pretty much any of the barbarian factions will do, with units like the Chosen Axemen, Golden Band and Lombard Berserkers of the Alemanni, Burgundii and Lombardi, Gallowglasses and Hounds of Coulann of the Celts and the Heerbann units of the Franks.