What to do with bugs and fish?

I'm a fairly new player to Grand Bazaar, I'm still in Spring, and I honestly don't know what to do with the bugs and fish I catch.

I know I can cook the fish and sell at the bazaar, but storing the bugs to sell at bazaar takes a lot of my limited space.

I don't want to look up too much because I don't want to see too many spoilers, but is there any kind of collection museum or similar?

Basically, what do I do with all the bugs and fish I catch?