So we are thinking of making a store of characters with coin within the game, it could give us a direction to follow like we want the player to earn coins at the end of the matches and then save the amount of coins and also save the characters that the player buys.

What is the best way to do this with this engine?

For saving and loading, you could add a "coins" value and "locked_characters" value to the "stats_load" scripts, which will allow you to use the "stats_*" functions. You can also just use default methods for saving and loading data (look up GMS2 tutorials).
In order to handle locking/unlocking characters, you'd probably want "obj_css_zone" to check the "locked_characters" value to see if its character is locked or not.