Enneagon: It's a long time since I played, so I don't remember was there significant difference between first and second game in this regard, what follows is true for Lords of the Realm 2:
Peasants
Very cheap and very useless. Avoid to use for combat. Can do some damage if outnumber opponents at least 4:1 and mange to surround enemy in detail. Can be used to fill in moat.
Best use: split out very small detachments (by exploit of castle garrison you can even split 1 men armies) then use to suicide-scout enemy forces, slow down enemy armies (by blocking roads or their way otherwise), demolish opponent fields and services.
Pikemen
Defensive unit, best hand-to-hand defence. Cheap. Very slow. Low damage.
Use to form defence lines and block choke points in front of your archers. Can be used to fill in moat.
Operating pure Pikemen unit is possible, but hardly the most effective way of deployment.
Archers
Most likely will form core of your army, using all other units to service them. Beat anything in large enough numbers. Long range low damage attack, helpless in hand-to-hand. Avoid deployment of pure archer armies, except, probably as castle garrisons (but having few Pikemen or Swordsman may be advisable in garrisons too).
Maceman
Poor man's cavalry. Cheap, fast, deadly - first hit from movement can score multiple kills, but fragile and vulnerable to ranged fire. Use to target enemy archers, peasants, flank or back. Can operate on their own, especially against peasant/archer armies and/or when outnumber opponents.
Swordsman
Good in anything, excels at nothing. Probably best ranged defence. Expensive, but often worth it. My most "standard" army is formed from equal numbers of Swordsman and Archers. Can operate alone, but not to the best efficiency.
Crossbowman
Short ranged attack, deadly - every hit score a kill, surpassing defence. Expensive. Very weak in hand-to-hand. Can't replace Archers in general ranged role and only make sense as contemporary unit in larger army or garrison, but as such is great addition when used for best effect.
Knights
Very fast, probably best hand-to-hand attack. Ridiculously overpriced.
Best use: catch and kill enemy archers in preparation phase movement, or outflank them after infantry clash; run for castle flag. In theory, can operate alone, but you unlikely will deploy them like that.
It makes sense to produce knight armour to be sold for profit.
Thank you.