I have a small collection of those things I said.
Some fossils I have found on my own (just small fossil shells and sea sponges).
Once I discovered a patch of fossilized shells at the top of the Grand Canyon!
But I only took photos as it is a national park and you are not allowed to remove anything. But still, I decided not to tell a soul the exact off-trail location because they would be chipped out whether by fossil hunter or park geologist.
My collection is small but I do have the usual stuff. As well as a couple of more interesting things, such as a fossil backbone piece from a....I think a hadrosaur.
From the rocks, I think my fave are opals. They really catch the light with their "fire". I have mostly cut and polished cabochon opals (nothing expensive, mostly cheaper Welo opals from Africa), but also some raw ones from Australia. I have some chunks of lava rock of different types (including splatter), I picked up off the ground for myself in Hawaii and Iceland. Supposed to be bad luck, but I do not believe in luck so whatever.
Meteors, I have a little bit of pallasite but mostly the usual iron-nickel, some with regmaglypts.
I got to touch a piece of the moon once, when I visited NASA Kennedy Space Center. But of-course hundreds of thousands of people had touched it before me so I was probably only touching the build up of oil from their hands.
The collecting has resulted in my always staring at the ground when others I am with are looking at the view far away.