Ys III is an entirely different story which has nothing to do with the first one. The only thing that ties the two together is that a few times in the game people speak of how amazing the main character is for what he did in the first game. Other than that there are no references made to the first 2 games at all. It really wouldn't spoil or ruin anything if you played through the 3rd one first.
Absolutely correct.
BenG76, you don't have to worry, but we will understand if you play Ys I & II first, regardless.
SUGGESTION: At the very least, you should listen to the songs in Ys III. Skip the audio for the cinemas, but definitely enjoy the tunes!
Ys I & II have the best soundtracks, but Ys III is friggin' awesome, too.
Don't listen to folks who say Ys III's soundtrack is superior to that of Ys I and/or Ys II. They're mistaken