OK, this response is super late (I know you posted this a month ago, and you've probably navigated this issue since then), but maybe this can still be useful to you or someone else looking for help on this topic.
I think for a beginner who is struggling to balance gameplay and story, this method could be useful (certainly is for me!):
Result: "Match-3 puzzler about animals"
Result: "Gameplay: match-3 with contextual combos. Story: Animals being sold in a pet store."
Your brain is probably already churning with little ideas from step one - jot them down!
Result: "You play as a pet store owner trying to sell his animals, in a match-3 puzzle grid format. As the game progresses, contextual/trickier combos can be made to increase your score. Sell (match) three cats and three mice side-by-side for a 'Tom and Jerry' combo, or put a snake between a lizard and a fish for a 'Scaly' combo."
Result: "Linked concept - Feature: In some stages, animals come in male-female variants, and there is a 'breeding' combo - dragging a nest between a blue and pink bird makes chicks, which are needed as part of the level goal. Story: The store owner is running low on stock as his business booms, and starts to breed his animals to increase stock."
You might find it easy to write out a list of features and a list of story elements, and see if anything seems to click together. Sometimes they will go hand in hand and seem really obvious - a bulletin board for adopting strays (story) naturally goes well with a daily challenge system (feature). These are the best ideas - because they seem natural and logical to you, they'll probably be natural and logical to the player learning that mechanic. Don't wrestle to make something work if it doesn't fit!