They're like Final Fantasy in that they're not really connected story-wise, so starting with any can work. Etrian Odyssey Untold: The Millennium Girl is a remake of the first game so it can show you the root of the series if you feel so inclined. If you don't care about beginning with the original then Etrian Odyssey IV is probably the overall best in the series with more refined gameplay and mechanics, as well as more accessibility features to help newcomers. The one I would recommend to not start with is Etrian Odyssey Nexus which is a mashup of the entire series and is better suited to longtime fans.
These games have gone on sale in the eShop several times before, so I'd wait and see if Atlus does any more sales before the shutdown, they probably will.