I'm a newcomer to Ys, and I just finished Ys I.
I am going planning on playing the games in this order:
Ys I Chronicles + > Ys II Chronicles + > Ys Origin > Ys: The Oath in Felghana > Ys VI: The Ark of Napishtim

Unfortunately, my ancient PC can't play DirectX 11 games (which Celceta is) and can only play up to DirectX 9.
I am playing the games for the lore and I don't want to miss out huge chunks of the story by skipping Celceta.

And no, I don't have a Vita so that's not an option.
Plus, my PC won't handle Lacrimosa of DANA.

Yes you can skip it but when you get a new pc you should play it because it is one of my favorite ys games. The only games you should play in order are Ys Origin--> Ys I ---> Ys II

Yes, you can play in any order really.
Celceta is a reimagination of Ys 4. It's the third version of it. If for the lore only, you can play the Snes or PC Engine versions. Currently I'm playing the PC Engine one, Dawn of Ys, as is the only version that remained to play.

You can play whichever game look interesting for you as all of the Ys games are completelly separate game with barely any mention of the other titles. Ys Origin, I and II are the only one that share story elements. Other than reused concepts there is no shared story in the other games with the mere exception of Ys 8 which mention the cronologically previous title as well foretell the next one but still with no story elements.

I know I'm years late, but this is a question that comes up a lot, so I thought to comment in case it helps anyone.

While Ys games do have a chronological order, the events of each one are self-contained. The only ones that directly need to be played in order are 1 and 2, because they're one story that got split into two games, but for the rest you can play them in whatever order you want. That said, some games make references to other titles, and Oath in Felghana foreshadows the plot of future games, albeit very slightly, so while skipping games isn't that big of a deal, I do recommend playing the ones you do have access to in order.

This site explains it well.