Nice! We need them all!!
I Wonder if I'll miss something if I've just play'd the "first three ones" (chronicles and oath) and origin and I jump straight to the sixth one. I supose I will, oh well...
Actually, Ark of Napishtim stands really well on its own, so you really won't have much difficulty with that. Oath is a rebuilt version of Ys III (Wanderers from Ys) using the engine established in Ys VI, so in some ways Ark will seem a little more archaic. Not much though, and it's mostly combat-pace related. Ark is a smidge slower in some ways compared to Oath - not much of a difference at all, and very subtle, but it's there. Boss fights are about as intense.
Plot-wise, you've got nothing at all to worry about. The beginning seems a bit confusing, but it's not due to any Plot ties to prior titles, so no worries there. Ys Seven on the other hand has a bunch of ties and shout-outs to Ys VI, so if that were coming out instead of Ark I could see there being an issue. Not a big one, since the Ys games as a rule stand on their own very well, with the exception of Ys I+II which are pretty much their own two-part story and Origin, which primarily serves as a prequel to I+II with some shoutouts to other games in the series here and there.
Bottom line: You'll be fine.