My favorite part story-wise... I'd say that honor goes to Part 2, followed closely by Part 1.
What I love most about Part 2 (aside from managing to have a nice plot despite it only lasting 5 chapters) is how everyone has a reason for being there, and are all happy to help Elincia in her struggles. I love how it focuses on smaller characters too: Brom and Nephenee didn't have to get their own chapter, and yet they did; Marcia and Haar didn't have to have all that much presence in the plot (Marcia cheering up Elincia and accompanying her and Haar eventually joining them, etc.) and yet they also did. The dialogue where everyone supports Elincia during the Endgame right before battle starts is also a huge bonus for me. Overall, aside from a few flaws (the complete annihilation of Astrid's character and the way they just took Heather out of the plot for Chapters 1 and 2 for no reason whatsoever), it's just nice to see these characters shine a little bit on their own without Ike or Micaiah's presence. Like seriously, Lucia is a cunning one (sorry, not sorry, Ludveck), and I'm here for all of it. XD
Part 1 is a close second for me because I really enjoy Micaiah's character and her love for Daein, and I find it to be a very nice introduction to the game.
Gameplay-wise for me it's definitely Part 1. I love having to work with weak units and making them grow into stronger units. I love how during the first four chapters, if a unit dies, then it's automatically game over. For me it made it seem like everyone was integral to the overall success of the battle, plus I find that getting a game over is way quicker than restarting from the wii menu whenever someone died, although I'm aware that that's not eveyone cup of tea. Also, the ambience and overall feel that the "Dawn Brigade" battle music and the enemy's theme "To war" manage to create is my favorite in the entire game.
Moreover, this may sound weird, however I've always loved watching everyone's stats at the beginning (you know, like 7 magic, 7 speed, 5 defense, all those stas with only one digit) and watching them grow into 2-digit stats later on, which kind of felt like it simbolised their growing strength.
I've always especially appreciated the HP bar. Watching it grow from numbers like 15, 17, 22 all the way to 30 always made it seem like they had so many HP by the end, especially if the number went from 31 onwards. For example, even if it's not true, a 31-HP Rafiel seems to me like he could take more hits than a 28-HP Edward ever could. When that number goes over 32 it really feels as thought that unit has finally become someone difficult to bring down for the rest of Part 1. I don't know if this is true for anyone else, though.
Part 3 for me is a close second. I somehow manage to not always have the easiest time with the Greil Mercenaries in battle, which I wholeheartedly appreciate. They are very fun to control, and their chapters just run so smoothly. Unlike the roughness of Miacaiah's and Geoffrey's chapters, which I love nonetheless.
I love jumping form army to army. Just wish it was done more seamlessly, but hey, we still got what we did, so hooray for that!
My least favorite part has to be Part 4. Although I love Yune and Ashera, the road to the tower just ruins it for me. Honestly, no support conversations and NO info conversations while at base either aside form the main characters?! How can you mess up at writing so much?! This was already a problem during Part 1, where the others (Leonardo, Edward, Nolan, Laura etc.) never reacted to the laguz ruing, to joining the Daein Liberation Army, or even just reaching Daein Keep. This was especially a problem since their characterisation is close to non-existent.
However here there is no possible excuse. Path of Radiance had loads of great characters. What do the minor characters have to say about their current situation? Why is everything a boring rout mission with endless reinforcements? Why couldn't they come up with something more creative in terms of map objectives or plot during the en-route part? I'm honestly flabbergasted.
Every other chapter in the game felt as though it had its own personality, while here everything just feels... empty... I don't care that it's possibly on par with the world turned to stone theme. Everyone in the enemy army is human, for crying out loud. How does it manage to be so black-and-white?
The bosses are still fun to kill and bring down, at least (I'm referring form Valtome onward, obviously). Also, the Endgame, although far from my favorite, is great as well.