If the system has things you gain go with what the system says, unless you enjoy adding twists based on their adventuring, I do.
I love that montage and flavor idea, yes that works.
But in a game with little actual crunch in advancement think of advancement things like Magic Items. That kind of enhancement mechanics trapped in physical objects in the fiction can be unlocked from physical items.
Say in an adventure they encounter a smithy who if they save their life or have some other significant effect on their life could offer to show them how to get the effect of say a +1 sword against a type of armor. A variety of things like that, from experiences in the adventure, give a menu of options to choose from. That's probably the most powerful kind of example. It can be super tricky and you become a game designer but that's part of the fun.