No items should be tradeable, as this removes their value.
The items should be for fun, possibly a special gif, but not for serious things (killing people, etc) as this takes away from the paid weapons.
If you make it for one thing, you should make it for another.

Digging,
Crab champion, an item like the zombie crypt trophy (standing on top of a pile of dead crabs/broken shovels)
As well as this they could have a special room where there are multiple cool looking skins (gold shovel), with the same stats as a normal shovel, just looks better.

Pizza,
Pizza cutter and chef hat?

Car missions,
Able to purchase a special car with a nice looking racing helmet.

Mining,
Miners hat and again with the skins idea.

Mushroom picking,
Shroom hat with a hallucination gif (varying colours, moving)

Trash picking,
Nice looking trash pick, something else?

Did I miss anything?