Unlike some of the other games apart of the Fire Emblem Series, it is always recommended to promote a unit as soon as the option becomes available to you. Without a tremendous amount of investing, odds are one single unit will never reach the Level Cap of 20 at their highest tier class before the end of the game.
Furthermore, should you promote a higher level unit, the less they will benefit from the base stats of their promoted class. For example, a Villager that promotes to the position of Mercenary with 5 Speed and a Villager that promotes to the same position at 10 Speed will both have 10 Speed after the promotion.
One exception to this pertains to Alm (who can promote when Celica reaches a given point in Act 4) and Celica (who promotes automatically after her completion of Act 3). As the main characters of the game, these two are much more likely to be used compared to other characters. These two also have excellent growth rates when they stack up to others, which makes it wise to also wait until Level 20 before promoting them.