Starting out strong!
I came late to the Fire Emblem franchise, and decided to start with the first one, even more then a decade later. And I was really impressed by how it's still an amazing game that holds up well.
The character diversity is really well made, I can't remember any other franchise with as many types of combinations for characters, classes and their weapons, that still feel balanced for the grand majority of it. I liked how they split the story mode, and how they made the presentation, moving from chapter to chapter and having dialogues in between to tell the story. I thought it was really well written, but the plot overall was just fine.
Where the games shine the most is in the gameplay department, the tactical dept of the combat. Being turn-based on a grid-system, having a rock-paper-scissors type of strenght and weakness. For melee combat is Sword-Spear-Axe, forming a triangle for the player to decide who to use against each opponent. The magic system also has it's own type of triangle system of advantages.
The part of the game that it hooked me, was with the leveling system. Each character earns experience by attacking and opponent, the more damage it deals, the more experience it gets. When you get to a certain level you can upgrade that characters class to a stronger version of it, but you need an specific item to do so, based on the type of class of said character. The longer you wait to upgrade it, the higher of a cap his stats can hit, because when you do it, it's class level is back at 1, but his stats just keep going up.
Another big part of the franchise is that it's a permadeath game, if a character dies, that person is dead and the story moves on. Unless the protagonist dies, then it's Game Over. It's possible to restart the chapter any time, if the player wants to have a no death run through the game, but it's really hard.