I\'m thinking about filling a collection with a large amount of unique objects. How is the cost of an insert in a Set (say HashSet) compared to an List (say ArrayList)?
You're right: set structures are inherently more complex in order to recognize and eliminate duplicates. Whether this overhead is significant for your case should be tested with a benchmark.
Another factor is memory usage. If your objects are very small, the memory overhead introduced by the set structure can be significant. In the most extreme case (TreeSet vs. ArrayList) the set structure can require more than 10 times as much memory.