Origin spoils the well, story of 1 and 2, so if you're going to play them, play them in this order: 1, 2, Felghana, Origin.
I don't think it really matters.
According to an XSEED guy that posted on SPUF:
"Yeah, you should have no problem. Since it is a prequel, it's technically the earliest point in the story, meaning there's absolutely NOTHING you need to know going into it.
The worst case scenario is that some very minor plot points from Ys I & II will be spoiled for you by playing Ys Origin first -- but as with most Ys titles, it works both ways: if you play Ys I & II before playing Ys Origin, it'll almost feel like those same plot points are spoiled for you in Ys Origin."
Oh, it does. One particular bit of story in Origin won't have the same, well, emotional impact, unless you've played and beaten Ys I. This bit of story actually made me go "Wait, what the crap?!" since I wasn't expecting THAT to happen.
The other reason is the fighting system. Playing Felghana and Origins, then playing 1 and 2, will make you dislike 1 and 2 since the game styles are so different. Origins and Felghana have a much better game system than the old bump style (and Felghana's is much better than the absolute mess that was Ys III.)