When matters turn from bad to worse, you'll want a large army. Unlike mercenaries, army units also require food, which you can harvest with peasants. However, don't ignore spies, envoys, and other units once war is declared. You still need to keep your economy going even in the midst of battle.
Men-at-arms are your basic foot soldiers. They're great for laying siege to towns.
Strengths: pikemen, horsemen
Weaknesses: bowmen, crossbowmen, knights
Pikemen are generally weak in battle, but they're very effective against mounted units.
Strengths: horsemen, knights
Weaknesses: men-at-arms, bowmen, crossbowmen
Bowmen perform well against slow moving units.
Strengths: men-at-arms, pikemen, crossbowmen
Weaknesses: horsemen, knights
Crossbowmen, on the other hand, excel against armored targets.
Strengths: men-at-arms, knights
Horsemen easily run down ranged units, but don't send them against armored units.
Strengths: bowmen, crossbowmen
Weaknesses: men-at-arms, pikemen, knights
Knights are arguably the strongest unit in the game, but they aren't without counter units.
Strenghts: men-at-arms, bowmen, horsemen
Weaknesses: pikemen, crossbowmen
Clearly, no one unit will win battles on its own. There's nothing more frustrating than investing most of your resources into a strong mounted army only to realize that your enemy's protected by a number of pikemen. Gathering intelligence on your enemy's armies cna help you build the appropriate counters, but if you can't find out what your opponent is up to, simply build a few of each unit so you won't be completely defenseless.
Commanders are the final type of army unit. While commanders can't do much on their own, they provide powerful buffs to surrounding units. If you purchase upgrades, you can give them a very helpful healing buff to keep your units at peak performance.