I've been writing fanfiction for some years.
You definitely want to go with the second, since Ao3 automatically sorts by date updated. While you're publishing, you will get new readers each chapter, and once your story is complete, you will then get the readers that only want complete works. Your second option is the best of both worlds.
Keeping your stuff "fresh" is less vital than on Tapas, since people frequently scour the archives, and there's no need to keep your chapters short like another commenter suggested, for that reason and because readers on Ao3 often prefer more thoughtful, longer chapters.