Best characters tend to be the Manaketes (especially Nah, and F!Moran if you play M!Robin), the Tacticians (access to almost every class and skill), and kids with Galeforce. Their builds will vary depending on their parents so I can't really say for sure, but if you want to test builds and stats, you can look here.
I borrowed my brother's game to try it since there are multiple files and now I am addicted. lol I didn't think I would like it because I am not really in to grid battle systems, but the characters are all really fun. My battle strategy is more "what would make a funny support conversation" than "what is the best way to win?" I don't get how you are supposed to level up the people who are too weak to fight though. If they support someone, they never get experience and if they are just next to someone, they are attacked and killed. Good thing I set it to casual. I wouldn't have a team if I didn't. heh heh
I kind of want Robin to marry Virion, but there are a bunch of characters I haven't met yet. What if someone is cooler? I don't like any of the choices for Chrom though. How come he doesn't have as many choices in support conversations? Should I just pick Sumia or the last character who I didn't meet yet? I just played the mission with the cute dragon girl and Chrom can't marry her either. Gyaah Chrom!
I had a similar experience. Strategy games are not something I usually go for, but my friend encouraged me to try the demo and buy the game and now it's the game I obsess most over. I draw it more than my unit more than anything else lately. And for the past year or so.