It find it extremely important to teach them the principles behind those (or similar) data structures first, and I'd go so far as to pick any one of the more complex ones as well (0/1-trees or even B-Trees etc.), just for fun (maybe skipping some details, if time is an issue). I'd also stress some "outliers" like ones that have O(1) in some of their operations; or at least one that is good not only for fast random access, but also for storage on slow media.
You did not tell us which kind of students you have (high school? University? CS or "Programming"? I'll assume CS at a beginner level.). But they will be able to find out how to use the API of their language of choice just by reading the reference documentation (or, alas, these days, more likely, some online "tutorial", which leaves away all but the barest syntactical information). The reference documents will also tell them a little bit about when to use which, but not quite in a way that compares all of the (theoretically possible) structures side-to-side.
That's your job: show them what the world has to offer, and have them get a gut feeling for when to use which. There are several aspects: O-complexities of the operations (insert, delete, search, ...); space-usage aspects; aspects related to storage (i.e., is random access cheap or not?) and so on.
I find it very important that you are able to teach them on a board or paper; i.e., draw boxes, draw lines and so on, so they really get an intuitive feeling about all of this. After that, the actual implementation of most structures and operations should be a snap; and using pre-made libraries even more so.
Whatever you teach them in this way will stay valid and useful until the end of their lives. It gives a good foundation and reinforces structural thinking, branching out to the algorithms later working on those data structures. It's the same reason why one would rather teach a handful of abstract sort algorithms instead of the Java SDK functions for sorting.
For me, a solid knowledge about data structures is one of the few parts of my CS education (which is a few decades gone) that stays with me until today, and has almost everyday applications in both software development, analysis, design, architectural work etc.; and I have certainly, in the past, implemented complicated data structures without having to resolve to libraries (when there were none in the language at hand) with confidence, having a sound background about these topics.
I see no disadvantage with teaching how to implement those structures, whatsoever. I'd rather have someone teach only structures with not a single line of code; than a lot of code in a language or library which is likely obsolete in short time anyway, and no solid foundation for it. Have them find out how to use the API of their choice in their homework assignments; they should definitely be able to do that with any modern, well documented language (and if they are very young, give them a few handy pointers, like the names of the relevant packages/modules in the library or something like that).