I have never played a Fire Emblem game but was very interested in grabbing this as I was lacking a new RPG in my life. The game is absolutely addicting. The relationship dynamic between you (the professor) and the students adds great story based dialogue that feels like it matters. I chose to start with the Blue Lions and the character development of these characters has been some of the best storytelling you could hope for and according to few articles I read this is even the "least exciting" storyline due to its traditional story progression. So I'm excited to go through Golden Deer and Black Eagles.
I see a lot of complaints about some graphic issues, but honestly I haven't found many unless I was looking for them. The cutscenes like animations are beautiful.
Combat is very fun, I choose classic mode, which means permadeath to those in my company that die in combat which makes me try a little harder than I normally would. The class system is great, I do wish I had a few more options in the later classes (Master classes). Tier 3 (Advanced classes) definitely seems to have the most diverse set of classes.
Note:If you haven't bought the game or haven't got that far, the Fortress Knight class makes a character and absolute monster. Try it, and laugh as your enemies bounce off of you like bugs on windshields on the highway.
If I had to make a change it would be to the explore option on your character's day off. This allows you the professor to do small quests inside the monastery and interact with students of both your class and other classes. For someone who enjoys trying to do everything you can, having every conversation and participating in every quest gets reptitive.