Recommend me a game to get me into FE.
If you've never played an SRPG in any capacity, I recommend starting with Awakening, then play the rest of the 3DS and Switch titles in release order. Which would be
Awakening ->
Fates: Birthright/Conquest ->
Fates: Revelation ->
Echoes ->
Three Houses ->
Engage. I would hold off on Engage until after you played more games in the series, though, as the fanservice pays off a lot more if you have a handful of classic/modern games under your belt. Honestly though, other than
Fates: Revelation (since it's the golden ending) you can't really go wrong starting with any of the contemporary games, because they're all super welcoming for newcomers, yet they still offering engaging gameplay. Either way, I'd recommend
Awakening, it was my first FE game, and was a blast every step of the way.
Otherwise/after the 3DS & Switch games I'd go with the GBA games, as they're the perfect middle ground of classic and modern (ignore that they're 20 years old) difficulty. You could start with FE6 (
Binding Blade), but it's more difficult than the two games that follow. If you've played all the 3DS/Switch games already, then you should be fine, however, if you want to familiarize yourself with the mechanics of the GBA games then you can go with FE7 (the one localized simply as
Fire Emblem). It's a prequel to FE6 anyway so you don't lose out on anything by starting with it. Then you can move onto FE8 (
Sacred Stones), FE8 is widely considered one of the easiest games in the series, so you could probably start with that one as well. Following FE8 you could either go with FE6, or if you played it already, move onto the Tellius games,
Path of Radiance, and
Radiant Dawn on GameCube and Wii respectively, After those it's the DS games:
Shadow Dragon, and
New Mystery of the Emblem, which are remakes of FE1 and FE3 respectively, the latter of the two being the first game with casual mode.
Lastly, there are the Famicom/Super Famicom games; FE1 (
Shadow Dragon and the Blade of Light) and FE2 (
Gaiden) on Famicom, then FE3 (
Mystery of the Emblem), FE4 (
Genealogy of the Holy War) and FE5 (
Thracia 776). Since you've played remakes of FE1-3 at this point, you should have no problem with the originals, even if they're much clunkier in comparison. As for FE4 and 5, other than FE2, they're easily the most unique games in the series, which is why they're best saved for last (other than
Engage). With FE4, while it's chapter list may be small, the chapters themselves are MASSIVE. That may sound daunting, but you can save every turn, so if things go south at the home stretch of a chapter, you don't have to start ALL the way at the beginning. As for FE5, not only does it take place in the same universe as FE4, it takes place DURING the events of FE4, specifically between the 6th and 7th chapters. And before you go "oh cool, maybe I could play FE5 in the middle of those two chapters then go back to FE4!", don't. FE5 plays completely differently than FE4. It plays much more like a traditional FE game than FE4 does. In fact, in many ways, it's a progenitor to the GBA games, as FE5 introduced things the route split, fog of war, escape maps side chapters, poison weapons, etc. which the GBA games would all make use of in some way. Even the map design philosophy is quite similar. That being said, FE5 is a BRUTAL game. The biggest hurdle is probably the fact that you're broke for most of the game. Unlike other FEs, there are no bullions to sell, or money randomly given to you. So how do you buy weapons, or vulneraries? Well, that's the neat part, you don't. You're a small band of rebels, where do you think you get you resources from? You gotta take what you can, WHEN you can, which is where the games defining mechanic, capturing, comes in. In short, if your units constitution stat is higher than the enemy's, you can try capturing them. The catch is, your stats are halved when attempting this (because you're trying to hold them), if you're successful, though, you get to take everything in their inventory. And that's primarily how you get more weapons, staves, and healing items. There are some caveats, like mounted units not being capturable, even still, capturing is a remarkably powerful mechanic, and adds such a deep layer of strategy to the game. Every move you make is influenced by your ability to capture in some way, as you constantly have to consider whether taking the risk is worth it or not, while fully knowing you're constantly strapped for resources.
There's so much more I could say about FE5, because it's an incredible game, but this has gone on really long already so I'll end with this: while FE5 does throw a LOT at you, to the point where the game feels like it's playing dirty, you have an equal amount of tools at your disposal, it's just up to you to figure out how to use them. And when you do, it's super rewarding. Again, just don't play it in the middle of FE4 because of the aforementioned gameplay differences. It's also like 30+ chapters long when you include all the side chapters, and the route split, so going back to FE4 after how dense FE5 is would be like going to another planet. Either way, both games are fantastic, and some of the best the series has to offer.
Yapping aside, I hope that whatever FE game you start with, you enjoy the series. It's one I hold very close to my heart.
Also TLDR playing order:
Awakening -> Fates: Birthright/Conquest -> Fates: Revelation -> Echoes -> Three Houses -> Engage -> FE7 -> FE8 -> FE6 -> FE9 - FE10 - FE11 - FE12 -> FE1 -> FE2 -> FE3 -> FE4 -> FE5
