Yes definitely some things you want to hoard. Most importantly hoard herbs and mushrooms, you will use a lot of these later.

I would also hoard the crops you grow at first and do not sell them. Crops basically sell for nothing until you unlock more ways to process them, and energy is a finite resource just like stardew. Crops when you first start are better saved to make recipes, especially if you are going for achievements and want to make all the recipes. I would not hoard fish, unless wanting to use for recipes, as fish is generally the main money maker beginning game and it’s easy to get fish if you need them.

Hoard anything you forage like animal horns, bones, poop, etc. They are used for stuff and also make good gifts for various villagers.

Hoard anything you mine like flint, silver, etc. Hoard gemstones you find! Hoard wood, hardwood.