Just as my title states. I'm only focusing on the storyline instead of online battles. Should I pay attention to the natures or no? What do you think?
No, they matter little to none. Because you can level up to beat any for in the game IVs, EVs and Natures aren't necessary to keep an eye on ingame. Most of the time it will just be a waste of time to find a Pokemon with the right Nature as you will do just fine with any Nature. The same goes for EVs and IVs. But if you want a competative ingame team, it is recommended to go all the way. Just having the right nature isn't enough competitively. So my final recommendation would be to go extreme in either direction, if you play ingame don't bother with Natures but if you play competitively go balls to the walls with IVs, Egg moves and all that stuff.