If you're worried about difficulty or permadeath, awakening or three houses are probably best. Both are fairly beginner friendly, though they also have a lot more life sim stuff (especially 3H.) Fates is alright, but the story is awful. Genealogy of the Holy War is the first one worth playing, the first three aren't great unless you're interested in seeing the origins of the franchise. 5 is a slog and so is 6, though 6 at least has some good supports and hates you a little less. 7 is really good, it has a tutorial that goes on way to long, but is still very fun. 8 is pretty easy, but has permadeath and the world is different enough from the others that it's worth playing. The gamecube and Wii games are probably the best in the series.

Most of the games take place separately, so order isn't too important, but 1 and 3, 4 and 5, 6 and 7, and 9 and 10 are all directly related to each other, to different extents.

Edit: It also depends on what consoles you own. Obviously there you can emulate the earlier games, but the 3ds games don't always work on citra, and I don't think you can emulate three houses.