All the pros of the show have been expressed in this thread so I need not say why I adore the series, have done from the start. And I found all the characters appealing.
You think Faye's a bitch, but as the series progresses we learn why she has a barrier to stop anyone getting too close to her. She was hurt, betrayed, royally screwed over. I think experiencing what she did (cryogenically frozen ((<- spelling?)) and waking to find massive debt in her name) it's understandable she'd happily screw anyone else because to a wronged person I guess it seems fair. (I don't know, I'm not that way inclined.)
I love Faye. Man, she was probably my first anime crush (, or did I see NGE first which would make it Misato?). Darn she's hot. I mean her habits leave a lot to be desired but she's real. Women aren't perfect, people aren't perfect, and I love how the show demonstrates the characters flaws as well as the good/admirable traits.
As for fave episodes, there are some fantastic episodes but those that deserve a mention are Toys in the Attic (good fun), Jupiter Jazz part 2 (awesome and Faye in THAT dress.. *nosebleed*), Pierrot Le Fou (flippin' creepy!!), Cowboy Funk (excellent. Funny stuff!), The Real Folk Blues part 2 (action packed, emotionally charged, very impressive).
Hmm.. guess I coulda tried to narrow it down a bit more.... naaaaaah!