Can I choose the order my collections are listed in?

Yes. Open Art Studio, Collections. Under the list, Order On Your Website sets how your collections are listed on your website's Artwork page and on each work's page. A to Z lists them by name. Your own order shows them as a list you drag into place, so a series can come first. Press Save order to apply it.

Only collections shown on your website are in the list. A private collection is not on the website, so it has no place in the order.