All three Ys games worth playing on the PSP (I'd get Ark of Napishtim elsewhere if possible, like the PC version if XSEED manages to release that since it's by far the best) are very different, and all of them have their own strengths and weaknesses. So if you end up not liking whatever game you start with or have some complaints, it's still likely that you would like one or both of the other games. Ys as a whole is pretty much the opposite of Trails in the Sky in most ways. Fast paced action vs slow turn-based combat, emphasis on combat vs emphasis on story, shorter games vs long games, etc.
Others have covered the differences pretty well. Seven has some more traditional RPG measures thrown in like upgradable skills, lots of weapons to find and buy, a crafting system, etc. It's also significantly easier than both Oath in Felghana and Chronicles, and it's the only game where you have multiple playable characters. It's long, there's more text and story than most Ys games, and admitted this does get in the way toward the beginning. But once you're an hour or so in things are good until the last third or fourth of the game when it does drag a bit. Still, it's very fun to play despite those niggles, and works pretty well as a "My first Ys" type game.
Oath in Felghana is the better game on most counts, but it's tougher. Jumping means some platforming elements, no party members, less micromanagement, and lots of focus on some great dungeon designs and action. It's short and to the point, the story isn't great, but it's not very intrusive. This and Ys Origin (which plays very similarly) are my two favorite Ys games, and probably break my all time top-10 favorite games list.
Chronicles is old school and a bit archaic, but I wouldn't change a thing about it. No attack button for melee attacks, but Ys II does have a button to fire magic, instead you tactically ram into enemies to hit them. Not very story heavy and super cliche, but that's about what you would expect out of a game from the mid-late 80s. Ys I is kind of meh, but it's short with an old school challenge. Ys II is fantastic though, and probably my third favorite game in the series. Overall it's just a really charming, old-school experience.
As for Trails, yeah, it's pretty slow for the first half of the game. But damn if the second half isn't excellent. If SC and beyond follow in the footsteps the second half of Trails FC, this is certainly one of the best RPG series out there. Not that the beginning of the game is kind of bad, it just doesn't really motivate you with a "big story" like most RPGs do and as a result it causes some people to find it boring. But the events at the beginning of the game are still important, the game does a great job tying everything together.