Pick a few characters you like and work them hard. Fewer, strong characters are better in the story mode than a lot of weak units, especially with Pairing Up (which you should thoroughly abuse). You can easily "catch up" weak units with the DLC maps (the first free one is great EXP for anyone who hasn't been unpromoted), so don't worry too much about letting your units "fall behind".
Also, don't be afraid to use better weapons as you find them. You can buy unlimited of pretty much anything except the better Throwing Axes and Javelins/Spears, so if you happen upon a Killer weapon early on you may as well use it!
An unlimited number of Promotion and Class-Change Seals can be bought from certain stores as you progress through the story line so don't worry too much about saving them for new units.
Change Seals (Second Seals) work like this:
If you're an unpromoted class, you can use one starting at level 10 to change into any other unpromoted class available to that unit. Every unit has a unique combination of classes they can switch to, so find out and figure out skill builds you want.
If you're a promoted class OVER LEVEL 10, you can change to any other class (Promoted or not) available to that unit.
If you're a promoted class UNDER level 10, you can change to any unpromoted class available to the unit, much like point 1.
Change Seals reset your level to 1 (and you keep all your stats, minus the minor tweaks that you get for changing classes).
Unlike previous titles, I HIGHLY recommend you promote or class change as soon as you hit 10 for T1 classes. This is because you learn both skills by level 10 (first one is at level 1) and you can always change classes over and over again if you're looking to stat-cap. On the other hand, you need to be level 15 for Promoted classes to learn their second skill (first one is at 5), so you should hit 15 on your promoted class (if you're looking for the skill unlock). Apart from that, there's no reason to ever go past 15.
Note that Taguel, Manaketes, Dancer, and Villager all learn their second skills at level 15 (and so you should class change at 15 to get some other skills before switching back to their base class, if you wanted to keep said base class).