What should I do with "collectible" items?

Solution 1:

It is as you said: aside from registering one of each collectible to the Collectopedia, their main use is for completing missions. There are many missions that require collectibles, usually more than just one of a kind, and often more than just one kind.

Unlike monster drops, collectibles cannot be bought with Reward Tickets. It is also not particularly recommended to sell them, since you can effortlessly amass larger amounts of Funds through FrontierNav. Unless you intend to buy high-end Skells for each of your companions or wreck your Skells often, you won't really need a lot of Funds.