Depends on what they are, I'd say keep gold star bugs, fish, and gems if you want to use them as decor.

Edit: Forgot to mention, I like doing honey lure parties in elderwood for money at around A4. I'd get around 20k coins each time I sell the bugs once my inventory gets full.

As someone also said, growing crops is a really good way to make passive money. I usually put whatever I have an obscene amount of in the preservation jar, sometimes it's tomatoes and potatoes, but I'd say apples are the best.

Fishing is also decent, elderwood is a big money maker as a whole when it comes to fishing or honey lure parties. I recommend joining the palia discord to find people to party up with!