My favorite episode is the one with Mikasa's backstory. The manga has so much more detail so I wanted her backstory in the manga.
I assume you are referring to the 6th Episode of Attack on Titan. This episode adapts both Chapter 5 and 6 of the manga and includes Mikasa's backstory. I'd also recommend reading the second volume of Attack on Titan: Lost Girls, which is also about Mikasa.