I started out with Awakening and, honestly, it seems like a good starting point. It basically has almost all of the good features from previous titles plus a few more (it was meant to be the last game, I heard, so they tried putting as much into it as possible).
When it comes to difficulty, Normal is pretty easy and Lunatic is crazy hard, so you atleast have the choice in that regard.
It has a really wide character roster, and probably the most varied one from the entire series (can't speak for Fates, I haven't played that one).
And when it comes to the story, it's not the most original thing ever, but it's still pretty fun to go through, you get plenty of characters all the time so you can have a big variety of strategies and setups, and the Support system encourages you to pair up different units together to make them stronger and see more dialogue. And I think the game lasted me about 30 hours-ish? It's a pretty decent length.
Whatever you decide to do, have fun!