There are generally two accepted orders:
Gameplay release order (which would be ys1 and 2, ys VI Ark of Napishtim, ys oath in Felghana, ys origins, ys seven, the upcoming port ys memories of Celceta, and then ys VIII), or actual release order ignoring remakes (ys 1 and 2, Oath, Celceta, Ark, Origins, Seven, VIII). There's also chronological order, but that's a little weird for a few reasons and is generally not recommended.
If you don't care too much though, you can basically start anywhere, except for ys 2 which is a direct sequel. The games are fairly independent otherwise, that just so happen to have a bunch of references going on in the background, that you might notice if you play in release order.
The only games missing are, as mentioned, the upcoming memories of celceta port, and ys V because it's in all likelihood probably going to be remade soon. Don't worry about the latter.