Ys games have crappy stories, anyway, they're all about the gameplay (and music.)
They're technically all prequels or sequels to each other, but each game is a new "adventure," so you won't feel completely lost.
Though VI is pretty sequel-y to V. So you might be wondering "Why the hell is Adol a pirate, why did he randomly wash up on this weird island, and who is this chick that I'm supposed to remember but don't."
Still, like I said, the stories are pretty lame, so don't worry about it. --- For those players who don't speak Australian, we have provided an English translation of the previous scene. Do you want to replay the scene?