This question has been nagging me for a while, and thanks to TeX - LaTeX Stack Exchange I have found an answer: Audrey's answer to the question What should BibTeX for arXiv entries look like? references the file biblatex-examples.bib where the entries baez/article and baez/online indicate how it should be done. If you are referencing an article, which also has a preprint, it should be like (this part I knew)

and if it's only a preprint without a published version (and not occurring in some conference proceedings or something), one uses the @online field (which settles my questions)

without any other frizzles such as url fields or something.

Actually, it is best to also use the eprintclass field for arXiv preprints, which is the main subject class under which a preprint is catalogued. This would mean you'd have to add eprintclass = {math.QA}.

Tomorrow I will leave for the Auslander Auslander Memorial Workshop, and I don't know whether I will feel like producing a long post on Thursday, which as you might have noticed has been something that I started doing since the first week of October. I have some drafts, but I guess you'll have to wait for those.

Maybe I will even try live blogging the event (or discuss the talks in the evening, or something, or write down some things during my longish train ride back). Who knows?