You can buy units from the training center for 50 silver (roughly level 50) or you can capture them from free battle and dungeons. Personally I would just wait until your stats are 50+ each and start investing seriously into your army using captured units. That way you can get troops of higher level for free.
Your commander level also seems to influence how much damage your troops do. It seems similar to your stats+cards in free battle. In army fights it's commander level + troop level+card rank. Try to make sure your commander level, troop level, and army size is superior to the army you want to attack before committing and always save first. Troops can not be healed and must be replaced after being injured. Once you commit a troop to an army slot, they can't be removed.
Army battles are mainly a large source of money, but if you defeat the most powerful army, you can purchase their captured princess at the training center later after a town event. She costs 50 gold and upgrades your sleep options in your home. You can fuck her, beat her, execute her, or free her. It also seems like sometimes she will give you bonuses when you return home. Once on returning she gave me a sword dancer to kill or capture.