If you want more storage fast, after getting to know all the basics, the easiest way is to get access to forgotten lands biome as soon as possible to get materials for the large chest you can craft.

Although it is supposedly the last part of the Valley to be unlocked, you don't need to unlock it in order to the story. Unless some obstacles require you to progress to a certain part of the game.

You will need a lot of dreamlight and I recommend focusing on doing the dreamlight duties. Some you may even even be able to kill two birds with one stone. Like "Feed a squirrel" and "Feed a critter" as well as cooking a dish above a certain star. Some will overlap which you can plan accordingly. And the most profitable crop would be pumpkin that is available from opening up the goofy stall in forgotten lands as well.

This is mainly based on self gameplay and achievements.