There are some situations where you want to promote ASAP while other situations where it's kind of... eh?
As an example: Gray is a Villager you get at Lv. 5. He will also be your main (potentially only) Mercenary promotion out of the starting villagers, as it's by far his best class. The base stats for Mercenary are as follows:
24 HP, 8 Str, 8 Skl, 10 Spd, 0 Lck, 4 Def, 1 Res
Gray's base stats are as follows:
24 HP, 9 Str, 4 Skl, 4 Spd, 2 Lck, 4 Def, 2 Res
That means that when you decide to promote him to his inevitable Mercenary, if you do it immediately, he will gain 4 skill and 6 speed. This is a situation where you don't want to waste time trying to get level ups, as instant promotion will help Gray become WAY more useful IMMEDIATELY.
If you don't gain much from promoting, you can probably stay in the class a bit. Example exceptions would be things involving spell lists (ex. If you want Faye's Dancer spell ASAP) or if you want to go into a high movement class (ex. Villager -> Cavalier)