I've been wondering this, too. Thanks for asking!
I normally make a sim collect certain stuff in a way to match their personality. I might have a sim collect only certain minerals or certain fish, trying to connect it to some personal backstory or agenda. Selling off everything that don't fit the bill. This way I avoid filling the entire house with collectibles. And - it's nice decorating a home in such a personal way. Using some shelves or display table, perhaps in a room dedicated to this hobby/obsession. It might become a household routine or tradition, for future generations to bring on.
I avoid storing collectibles in inventories, and I don't use the collect lists to check that I found everything in a certain collection, either.
PS: Collectibles can be good gifts to others.