Not all characters are created equal, as you'll quickly learn if you earn some highly ranked characters.
In addition to your base moves and upgrades, your characters will also have a star rank and - in case you haven't guessed it - higher rank is better.
More powerful heroes which do more damage will have at least three stars and up, and frankly, if you earn any of those, they're worth getting rid of other characters in your party for them.
Heroes of colour
The heroes you have in your party will each correspond with a gem that you'll be matching on the puzzle grid, and you'll have one of each.
A red hero, a yellow hero, a blue hero, and a green hero. What this simply means is that if you have a whole bunch of yellow heroes lying in wait, your favourite might not be the best.
It can come down to what attacks and abilities they use, but usually you're best off just using whichever heroes are the highest rank or have the most power.
Train, promote, upgrade
Going into each character in the party menu, you'll notice their base strength is not where things end. For every level you gain, you will be able to power up each hero once, for a coin fee.
That will keep them powerful. In addition to that, extra hero shards for your unlocked characters will allow you to rank them up, and special materials or regeants will allow you to power up even individual attacks.
It all costs materials and coins though, so you're best just upgrading the characters that you're actually going to use, and leave the weaker heroes for another time.
This will give you a big advantage, trust us.
One you reach player level 10, you will also be able to raise your heroes to hero level 10 each, and when each reaches this level, they will earn a passive skill.
This differs heavily between the entire cast, but this can give you defensive or offensive buffs, and will make battles way easier, so level 10 should be your first goal for your main cast.