Must-have Babylonians:
Nergalsharezer
Nebuchadnezzar
Nebushasban
King Merodach-Baladan (Make sure to have Carried into Exile)
Winged Lion (IMO)
The rest really depends on your playstyle. Archers of Kedar, Leviathan, Red Dragon, Gomer, Sapphira, Evil-Merodach, Babylonian Forces (if you have HQ at Riblah (which you should)), etc. are all good choices.
As for enhancements, some must-haves:
Head of Gold
Carried into Exile (if you have Mr. Baladan)
Nebuchadnezzar's Pride
Midianite Attack (especially if you have a good amount of banding)
Swift Horses
Deceit of Sapphira (only if you have Sapphira)
And again, playstyle will dictate the rest. Coliseum Lions, Sarah's Jealousy, Imitating Evil, Nebuchadnezzar's Dream, and a large selection of captures may serve as extra battle-winners, but I would save room for some of the delicious other stuff that only Crimson can offer, such as Belshazzar's Banquet, Great Image, Desecrate the Temple, Set Fire, and Arrogance.
