Build an army
You do not need to upgrade every unit. Some warriors are good without any upgrades, others need a little more armor or attack. Observe how the price of the unit increases as you upgrade the armor, or the attack.
Weak archers can be great even if they are lightly upgraded. But armored archers have the advantage of holding their line against cavalry charges a bit more and being useful in late game in flanking/attacking from behind enemy units.
Cavalry is a must. But do not spam cavalry because it cannot hold its own in prolong melee combat vs infantry.
Balancing the army
Best army is balanced army. Each unit type having its use.
Early game, most important are missiles and siege equipment. Catapults are very easy to destroy with fire arrows, so be sure to not rush them in places where archers could easily snipe them.
Protect your archers with a few strong cavalry and some spears. Spears are good at holding the line vs cavalry and have big bonus vs cavalry.
Infantry is best used late-game, where the enemy has low ammo. It is best to encircle the enemy forces, if possible and charge them using your cavalry in flank/back.
When fighting phalanx, attack them from multiple sides. You need to make the phalanx fight with sword. If your infantry is pushed by the enemy phalanx, it is best to retreat it.
Archers are very good at sniping cavalry, elephants, chariots and at shooting infantry in the flank/back.
Units with shield have bonus armor from front and left flank.
Elephants to not berserk but they are quite weak. When you are charged by elephants, put units in loose formation.
Against elephants it is best to use pillums/javelins.
javelin-throwing units can hide and are great in ambushing enemy cavalry or elephants.
Arcanii and Gladiators are great warriors. Use them as auxiliary units either to spring surprise attacks vs enemy cavalry or to attack the flanks/back of the enemy forces.
When fighting with cavalry against elephants, use your charge bonus and don't stay long in melee fight.
Make a formation in which your units can help each-other when needed.
Cavalry with spears has bonus vs cavalry but is weak vs infantry.
Cavalry when using sword and other non-spear units, has fast attack speed but no bonuses or handicaps. Best used vs enemy infantry or archers.