How important is an antique or collectible items provenance in terms of selling price and/or value?
That depends a little bit on the field in which you are collecting. In any case a good provenance can raise the price of an object. If you have two objects of the same quality, the one with the provenance should always be valued higher. In fields with many fakes (there are many, alas) such as for instance traditional African or Pre Columbian art, a good provenance can be very helpful. In the case of celebrities, the provenance can sometimes be the only valid criteria for the value of an object (Maybe hardly anyone would collect a piece of used soap, but if it was used by Madonna…).