Yes, the new Fire Emblem is very good, but a bit different. The game is split into 3 separate versions, Conquest, Birthright, and Revelations. The MC you create was kidnapped at a young age and raised in another kingdom, eventually your adopted kingdom, and birth kingdom get in a war, and you have to choose sides. Joining Nohr, which is your adopted family is Fire Emblem Fates: Conquest, this version is a more traditional Fire Emblem which means higher difficulty, and no extra maps to gain exp, or gold, so it's more difficult then Fire Emblem Awakening. If you choose Hoshido, which is your birth family then That is Fire Emblem Fates: Birthright, this version is more like Awakening, it's not as difficult, and you can do extra maps to grind exp, and get more gold. Then there is Fire Emblem Fates: Revelation, you don't choose either side, and you go off to try and find what force is pulling the strings behind the war, and try to unite your adopted, and birth families to destroy the threat. Each game is a full length Fire Emblem game at 27 chapters each, however the first 6 chapters are all shared between all 3 games. You have to buy the base game, either Conquest, or Birthright at full price ($40) then the other 2 version you can buy in game for $20 each. Keep in mind it's not 1 game split in 3, but 3 completely different full length games with different characters, and story, so doing all 3 will take some time.
This trailer video will give you a better idea, no spoilers, but will probably make a bit more sense if you watch it.
https://www.youtube.com/watch?v=me-9kWzxKoo
As for Primal, I also heard that it felt more like an expansion, rather then a separate game, so I will take your advice and skip it for now. Thanks.