There've been three distinct "playing styles" throughout the Ys franchise.
Ys I and II have the "bump system" where you walk around in a top-down perspective and instead of swinging your sword using a button you run into enemies from an off-center angle to hurt them without taking damage. (Ys II also allowed you to use some magic to attack) It actually works better than it sounds.
Ys VI: Ark of Napishtim, Ys: Oath in Felghana (a remake of III) and Ys Origin (a prequel to Ys I featuring ancestors of some of the NPCs you meet in the first game) are hack & slash action RPG's where you can jump around and (usually) use up to three skills as special attacks.
Ys Seven, Ys: Memories of Celceta (a remake of IV), Ys VIII: Lacrimosa of Dana and Ys IX: Monstrum Nox (not released in the west yet) make use of the party system with skills and up to three party members in the active party you can freely switch between.
You don't really play Ys games for the thrilling stories. Most of them are pretty basic where Adol arrives in some country, hacks his way through several dungeons and eventually takes down the god-like entity threatening the local area. There's some continuity between games, but not as much as Trails. The main selling point for the series is the fast-paced combat and rockin' soundtrack.
Ys I is probably the most dated. It's very short, has a level cap you'll reach about an hour or so into the game and has several obtuse "puzzles" you need to figure out by trial and error or by using a guide. Ys II refines the formula a bit and cuts back on some of the more unfair elements of the first game and is also a tad longer. If you can get used to the unorthodox gameplay system, they're still pretty fun for a rainy afternoon.
Ys VI: Ark of Napishtim is the first of the "Napishtim engine" games and is a fun, but occasionally rough around the edges in terms of levelling and certain boss attack hitboxes. It's still a fun hack & slash. Oath in Felghana and Origin are possibly some of the best hack & slash RPG's of that era and hold up extremely well in terms of gameplay. They're still a total blast to play and some people prefer them over the later games.
Ys Seven is like Memories of Celceta except slightly rougher around the edges. The story's slightly better, but not by that much. Some mechanics that got finetuned in Celceta are slightly rougher in Seven (like Adol being mandatory all the time, skills not having a feasable level cap and the charged attack that replenishes SP requiring you to hold down the button instead of auto-charging)
It all depends on what you're looking for in the games.
