With winter break on the horizon I'm highly considering giving one of the Japan exclusive Fire Emblem games. I've played, beaten and enjoyed all of the western releases save for Shadow Dragon, which wasn't terrible but had the misfortune of being the first game in the series that wasn't particularly updated when it was remade. I didn't think it was a bad game, but I found it underwhelming and kind of boring compared to the other games I had played before it.
Anyway, I'm hoping that a FE fan more hardcore than I could help me find one that I might enjoy. I am a bit wary about playing some of the earlier games due to the above but I am willing to keep an open mind. I'm considering playing Genealogy of the Holy War, since I hear that title is particularly well liked among fans of the Japanese games but I'm also considering giving Binding Blade a go if only for the sake of completing the GBA trilogy.
The Shadow Dragon remake was a straight up "port" like Ocarina of Time 3D and Wind Waker HD. I'm guessing that Nintendo figured that Shadow Dragon's performance and how people bought OoT3D mostly out of nostalgia isn't a good business plan, but you can blame Fire Emblem not being popular and apparently Oot3D was a quick development compared to Majora's Mask 3D which the devs said they have more time which is why bosses, fishing, and other stuff is being changed.
I don't remember what people said about Binding Blade gameplay-wise, but be aware that Roy, the main Lord, will be gimped for pretty much the entire game since he won't be able to promote until like 3 chapters before the end compared to Eliwood and Hector from Rekka no Ken/Blazing Sword which allowed the main Lord - you can choose which after beating the game - to gain more levels after their promotion.
Thracia 776 and Genealogy of the Holy War are solid, I think. I do know that Genealogy is really harsh considering the fact there's descendents and that since it's an older game it won't be as friendly as Awakening or even Path of Radiance and Radiant Dawn - I heard that Radiant Dawn is notorious especially on the harder difficulties.
There's also the Shadow Dragon sequel remake which is Japan-only. I don't remember if Shadow Dragon had a sequel and this is just a remake of the sequel or it's something expanded. I do know, however, it introduced the MU/Avatar concept, except in this game, they were decent units compared to Awakening where they're broken, but then again since you can max out everyone in Awakening, everyone was broken including the enemies (on Lunatic).
If you can get the games legitimately or find a way to support the devs, then go ahead. I suggest the Mother games as well for Japan-only Nintendo games.