Well... In the lore order I think it's: Origin -> Chronicles (Ys I and then Ys II, of course) -> Ys VI -> Ys Oath of Felghana.
Origin is a prequel fo the whole series, so yeah, it's obvious. Ys I and II are, too, obvious, althought you can't say that they are "next after" Origin events... But they have quite the connection with it. Ys VI being before Oath because of one of the characters from both games does something in the latter which would have impact, if it would happen before and not after Ark. It's a spoiler, so I'm not saying it, unless there is a spoiler tag.

EDIT:
There is not.

The bump system seen in a video might sound weird, but playing, maybe not. When I first saw it, didn't liked much, but after giving it a try, Ys I was the game that made me fan of the series.

About the order, for Ys I and II or Origin, it can be your preference, though in my opinion the best order is Chronicles and Origin after the first two. For Ark of Napishtim or Oath in Felghana it doesn't matter.

Isn't Felghana a remake of Ys III in a manner of speaking? If replaces the strange sidescrolling gameplay of the original with 'modern' Ys gameplay but my understanding was that it's role was still as part 3 of the overall series.

In terms of pure chronological order, it goes like this: Origin, Chronicles (I and then II), Oath in Felghana (remake of Ys III) and Ark of Napishtim. If you want to play them in this exact order, you're more than entitled to it, but I honestly would recommend leaving Origin for last, since even though it works as a prequel to the first Ys game, you won't get most of the references if you haven't played the other games in the series -- especially the first two.

Bear in mind that each and every one of the Ys titles available on PC (which GOG sells in their entirety, every other Ys game in the series isn't available on PC as of now, GOG and Steam sell all there is) stands alone quite nicely and can be played with no specific order or knowledge of the lore and story of the Ys world; they're more like super-polished arcade-action fast-paced games with some light RPG elements and a common setting, world and lore, but they *can* be played in any order because what binds them together isn't all that much to begin with, aside some minor references and the sharing of the same playable character and some NPCs (excluding Origin, in which you don't actually play as Adol Christin, the main protagonist in the whole rest of the series). Ys VI has some references to the previous game, Ys V, which isn't available on PC in any form, but even then the game itself explains the backstory quite well and you don't feel like you're losing anything, story-wise, by not having played the previous installment. Plus, each Ys title tends to be a story in and of its own, sharing only main character(s) and minor references that aren't all that important to the overall experience of the game.

Now, you don't seem all that interested in trying Chronicles, and I respect that, in all honesty I enjoy the post-Ark of Napishtim games way better than the first two, but do remember those games stand as a testament to the history and development of the Ys series, and the bump system, while sounding clunky and counter-intuitive when you're verbally describing it, actually works *very* well and adds to the fast-pacing Nihon Falcom always intended for these games -- much more so than the more "traditional" gameplay approach of later titles, to be honest.

People have certain personal quirks and "rituals" for everything they do, and playing video games isn't any different, so I understand why some would like to play them in story/lore order. If you're headset on doing that, just follow the order I stated previously: Origin > Chronicles (I and II) > Oath in Felghana (III) > Ark of Napishtim (VI) -- that's the correct order of all the Ys titles officially released on PC. Again, despite this, in order for you to fully appreciate some of the references in Origin, I'd recommend playing it last.

+1

A prequel by definition is meant to be given context by whatever it's preceding. Just because something is set earlier doesn't mean it should necessarily be experienced earlier.

To be honest I didn't know that. I 'found' Ys while it arrived at Steam, first. And due to events in Oath I thought it was after Ark.