I haven't completed the FE games I've played, but if I had to choose from what I've played, Awakening, Blazing Sword, and PoR stand out to me the most. PoR has solid gameplay and a decent cast and it's pretty challenging. Blazing Sword is accessible with a solid 7 chapter tutorial with complex enhancements, provides a solid cast (love Lyn), and solid gameplay that builds upon its challenge as you get better. Awakening builds upon everything that was established from previous games (weapons triangle, marriage and children, support conversations, map system, etc.) with new elements such as Second Class, new art, etc. It also did one thing that made it so successful, be accessible to newbies who just want to play instead of worry too much about dying and resetting. While challenge is great, the series wouldn't be able to go anywhere if it weren't for being accessible in Awakening and Fates.
i hope to play more FE games, especially Fates and Geneology.