The easiest iconic Star Trek prop to get is a screen used Tribble from the Deep Space Nine episode “Trials and Tribble-ations”. And Prop Store has one up now for $ 795. A bit higher than I would pay for this, but not unreasonable. I think this is a $ 5-600 prop because there are so damn many of them.
I got mine directly from the set photographer who sold his with a nice Letter of Authenticity. This one will come with a Prop Store COA. I do not know the provenance of this item, but I suggest you call Prop Store if you are interested. They are nice folk who will answer your questions.
You can find the item here.