I was in the same situation a few years back and did some research on the series. You can find the highlight below. Played through Ys 1-3, and I'm currently trying to find a way to play a translated rom of Ys 4 (PCE CD).
Before you start, just know that you would spend a lot of time grinding for EXP and money. You can refer to this article for details about each release:
http://www.hardcoregaming101.net/ys/ys.htm
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~ Ys Book I&II ~ ---------------------------------------------
Ported to and remade on countless platforms. The ones you may want to consider are:
TG16 CD (Available on Wii VC):
This is probably the best choice, and the one I went for. I enjoyed it so much, apart from the last dungeons of each game, and that's mainly because of their length and difficulty. They take up to about 50% of their games. I ended up using savestats.
Ys Chronicles on PSP / Steam:
Easily accessible on PC or PSP (which you would need for Ys7). Aside from the graphics and artwork update, the gameplay and story remain almost the same. I prefer the 16-bit graphics, so I went with that.
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~ Ys III ~ ---------------------------------------------
Available on SNES, Genesis, TG16-CD, and PS2 (JP-only), and remade on PC and PSP as Ys Oath in Filghana. Recommendations:
TG16-CD:
The only side-scroller from the classic releases, and it has mixed feedback. I personally enjoyed it. You may also want to check the PS2 version with the updated graphics, but I keep hearing bad stuff about the PS2 remakes, and they are Japan-only anyways.
Ys Oath in Filghana on PC / PSP:
This is a complete graphics / gameplay overhaul, but it basically shares the same story as the original. It's highly regarded and most of those who played it praised it, including fans of the original.
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~ Ys IV ~ ---------------------------------------------
This is probably where shit really hits the fan. There 4 different versions, and each has its own story events. Aside from the Vita one, they all remained Japan-only.
Ys IV: Dawn of Ys - PC Engine CD:
It's been regarded as the definitive version, but now that the Vita game is out, I don't know how it fares against that.
Ys IV: Mask of the Sun - SFC:
Considered inferior to the PCE CD version graphics and soundtrack wise, but you may want to give it a shot due to the different story events.
Ys IV remake on PS2:
The least liked out of the 4.
Ys IV: Memories of Celceta - PS Vita
Although it can be played on PS TV now, I'm still hoping for a port on Steam or PS4. It mostly got high scores from reviewers.