The very first episode I remember actually seeing was one of the really early episodes, before even Shippo joined them. It was the one with the frog demon who took over a noble lord's body and was about to eat the Princess. A couple years later, I saw my first full-length episode, a two-part filler about a half-demon who makes fake Shikon Jewels. I fell in love with the show instantly, and have been watching it since then.
As for a favorite, I don't really have one, but I adore Inuyasha, Sailor Moon (the original Japanese version), Mermaid Melody, Ah! My Goddess!, and of course, almost anything Pokemon. There are a few more, too.