Which Fire Emblem game should I play first on switch?

The simplest recommendation is that you start with Fire Emblem Awakening. Awakening was heralded as the series’ revitalization for a good reason. The gameplay is smooth, there are good areas to grind, and the story is solid.

Do I have to play the Fire Emblem games in order?

Fire Emblem: The Blazing Sword is technically a prequel to Fire Emblem: The Binding Blade, Roy’s game, also on the GBA. But there is absolutely no need to play that game first in order to appreciate this one.