Actually, I thought of another Fire Emblem game that fits: Fire Emblem Echoes. It's a remake of Fire Emblem Gaiden for the Famicom, which was released before a lot of things were codified into Fire Emblem. Unlike Shadow Dragon and New Mystery of the Emblem, Echoes keeps almost all of Gaiden's mechanics intact, including the awkward map design, characters that either move too slow or too fast, no weapon triangle, characters holding one item which can be a weapon or shield but not both, and only 1 point of speed necessary to get double hits in each direction, which means that it'll happen in basically every battle. Also, the enemies start out fine, but by Act 4 (of 5) you'll be facing an infinite swarm of powerful magic users that might randomly decide to teleport to your back line and gank your most vulnerable units, so that's fun.
The upside of all of this is that though it's a game from 1990, a lot of effort was put into making it look like a game from 2015. The updated art style might not be pure enough for the very few fans of the original game, but I think it looks great. The story, originally basically just 'go save the continent from the invaders and their mad god', now has actual depth and nuance to it, and the writing makes all the characters shine, both heroes and villains. Even the remixed soundtrack is incredible, and I've pushed through fights that I hated just to get to hear more of it. If you can deal with a whole lot of jank imported directly from 23 28 years ago, there's a very memorable and even fun game to be had. If not... just watch someone else play it on Youtube.