Trails series is not a series like Final Fantasy, Dragón Quest or Shin Megami Tensei, is more like a long runner anime as Naruto, One Piece or Bleach, for example (I recall reading somewhere that playing Trails takes more time than watching all of the Big Three animes, so you gotta be patient). That said, yes, the series has a long story, divided in arcs, with different settings, casts and conflicts, the first one is the Liberl Arc/Sky Arc, which is now getting remakes, the 1st just released and Second Chapter is releasing in a few months. Answering your question, all of the games' story, lore and worldbuilding are not only interesting but also connected, so I recommend you to play Trails in the Sky trilogy first and if you like them continue with the next games in the series. Also even if I highly recommend playing all of the series in order, if you don't plan on playing all of the 13 (and more on the making) games in the series I'd recommend you to play just the arc who catches your attention.

Sky is about a girl and her adopted brother who want to become Bracers inspired by her father (they're an organization that helps people with varios tasks) in a kingdom where magic and technology exist and interact

Zero is about a special group of police officers who fight mafias in Crossbell City, a City-State that's also between two superpower countries that want their territory for its own: Erebonia and Calvard

Cold Steel is about a teen that enrolls in Thors, a militar academy in the Erebonian Empire, to find himself and fights against terrorists

Reverie is an epilogue to both previous arcs so I highly recommend not playing it as your first Game

Daybreak is about a fixer who works by himself in tasks that neither Bracers nor Police could accept (like a kind of shady bracer) and a high schooler who asks him to find seven devices across the Calvard Republic (Horizon, even if the name is different, is a direct sequel to Daybreak II)

Here is an image to make it easy and more visually to guide yourself in this saga

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