I was mostly thinking of just using the same story from Super Mario 3D World but if that were the case, the game would just end up being a Super Mario 3D World Scratch Edition and I kinda wanted this to be original. I'm fine with using the same story but if anyone else thinks of a better idea, please let me know in the comments. Thanks :)
I think I have figured out the story. So, the game starts out just like SM3DW. Mario, Luigi, Peach, and Toad are all celebrating with fireworks and all that stuff, and they find a clear pipe. Mario and Luigi decide to fix it up. Then a whole boatload of items burst out of the pipe. Suddenly, Bowser Jr. pops out of the pipe and informs Mario that Bowser has been captured so Mario and Co go into the pipe to save bowser and the game begins. I thought of a twist in the middle of the game. When you at last release Bowser, he turns on you and teams back up with Bowser Jr. Essentially, the whole thing was a plan from Bowser. The rest of the game is just you defeating Bowser.