Best way to store an unordered list?
Within a database, what you're describing is a table. Tables do not have order, but the data can be indexed to allow easier maintenance and retrieval. 

You could always store data as a CSV list, XML, or a variety of other methods, but you should also consider what you're going to do with your data, and you're likely to find that a table ticks more boxes than most. If you're concerned about space, then compression strategies will help a lot, without losing the searchability.