I found the most useful unit while playing as Byzantium to be,
Byzantine Cavalary and Trebizond Archers.
The reason is that they are not that expensive for what you get. Byzantine cavalry is capable for taking out archer units, and for riding around and en-circling the enemy's melee units. For my infanty-line i use a mix of Spearmen and Byzantine Infantry.
Trebizond archers are also very useful because they are inexpensive, and can be utilized as 'melee' units when the situation is getting a bit desperate.
Usually my byzantine army would be as follows.
H/A H/A H/A H/A H/A H/A
A A A A
S S S S S S
General (and two units of Byzantine infantry/ or Cav)
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