I don't know anything about the Ys series apart from the fact that they're JRPGs. Just to give me an idea of how they play, what more well known franchise are the games most comparable to? Anything like Final Fantasy?
That LE sure is purty by the way.
Ys series are basically very fast-paced action-RPGs, but it's hard to pinpoint one series to call it 'similar to' because Falcom's always changing around how the games play. In the west, at least as of the time of writing of this post, there are quite a few games avaible, and many of them play quite differently from each other.
Ys I & II Chronicles, which is PSP/Steam right now, is basically a remake of the first two games in the series, but done so that the games would still feel kinda "retro", keeping the bump combat system that was unique to the originals. Instead of pressing a button, you basically ram into enemies from the sides in order to avoid damage and that's pretty much it! It's really simple and some people end up never getting too into it, but the whole thing works just fine. Other than that though, the Chronicles version of Ys I & II features a fully rearranged soundtrack by Falcom's very own JDK Band, and this is pretty much reason enough for anyone to play through those games. I & II have some of the most classic tunes in the series, with stuff composed by Yuzo Koshiro (of Master System Sonic/Streets of Rage fame) and Mieko Ishikawa. Your mileage may vary, but I am not exaggerating when I call it
one of the best videogame soundtracks of all time.
Next up, the two Steam exclusive games: (and then not really, forgot Felghana's on PSP too, thanks Magus) Ys: The Oath in Felghana and Ys Origin. The first one's a remake of Ys III, but done with a completely different mindset by Falcom. Whereas I & II Chronicles tried to keep the original's "charm" alive, with the retro combat and what not, Felghana is basically a new game with a good chunk of the story from the original Ys III. This is because Ys III was a game not loved by many, and even considered by some the black sheep of the series. The original played like Zelda 2, being a 2D sidescroller and all. Felghana basically ditched all that and works like a mix of action-RPG/hack'n'slashy combat with platforming, on a full 3D world. It was, before Ys Seven's release, my favourite game in the series, and definitely recommend it to anyone looking for a challenge. The game's HARD, haha.
Origin plays very similarly to Felghana, but it has its own perks as well. First, it's the only game in the series not to feature Ys' recurring main character, Adol Christin. Since it takes place thousands of years before Ys I & II and is a sort of 'prequel', there are actually three different playable characters! Also unlike Felghana, instead of a Metroidvania strucuture sort of thing, where new abilities allow to explore new places in the "world map", Origin is more of a dungeon crawler, with you going up and up on a pretty huge tower. Gameplay-wise, though, it uses the same engine as Felghana, so it's basically not very different on that front, except that two of the three characters have different styles of attacking compared to Adol (and Origin's Yunica).
Lastly, Ys Seven is a PSP exclusive and the first game released by XSEED here. Seven's probably Falcom's "biggest" Ys title, in that they definitely tried to increase the scope of the story. The game runs for like 25 hours, as opposed to the usual ~10, and it has a more elaborate plotline, with more cutscenes and what not. Mind you, the plot's still very oldschool, but the execution I felt was pretty good, so if you're into that, I'm sure you'll still dig it. The real star of the show here, however, is the new combat mechanics. Falcom dropped the Felghana/Origin engine once again and went for something completely new once again. This time, instead of just controlling Adol, you can have three different characters and change between them on the fly by pressing a button. They have different weapon-types that are more or less effective against some enemies, so switching is encouraged to best deal with some enemies. The game also features a more robust skill system, with characters learning quite a lot of moves exclusive to each of them, as well as other JRPG stuff like crafting new weapons and armors out of materials picked up from monsters in your adventure. Opinions on it are a bit mixed, with some of the fans saying they'd rather have the more straightforward nature of the old games and less story as opposed to this, but personally speaking, Seven's my favourite game in the series right now. I find the balance between story/gameplay pretty awesome, and just LOVED the new battle mechanics.
Last but not least, Celceta is following Seven's footsteps, keeping the party mechanic alive and what not, but apparently having a different 'focus', with exploration being one of the keywords in the game. I haven't played yet, so I can't tell you much about this one.
Anyhow, your best bet would be heading to YouTube and just searching for the games to see some footage of them, in order to get a better idea of how they play. As always, since this concerns Ys, I ended up writing way too much, but here's hoping it helped, lol.