Spike was--or if not first sight, at the moment he started mocking another vampire's claim to be at the crucification. Faith I don't recall for sure--I know I counted her as a favorite by the time I finished season 3, but I can't pinpoint the moment I decided I liked her.
But for several seasons, Buffy was just part of the backdrop for me. I always liked her--I had actually decided before I saw a single episode that I had to like her. Somewhere online, I had encountered a group of Spike fans quite viciously ripping into her. I was determined that this character, no matter how terrible she might be, was not deserving of that level of hostility. Furthermore, the whole idea of hating the most prominent female character in a show that you liked just didn't sound very fun to me, so I decided if I ever were to become a fan of Buffy the Vampire Slayer, I would at least like Buffy.
(Oddly, none of this Buffy-bashing put me off Spike. I figured if he was so popular, he had to have something going for him.)
When I finally started watching BtVS, I saw from the first couple of episodes that Buffy had a sense of humor and an attitude I could like, and so I concluded that I liked her enough and didn't think much more about her character than that. She worked as a protagonist, and she was likeable enough when she wasn't in the same room as her boyfriend (sorry, Bangel fans), but she didn't interest me a lot.
So for most of the first couple of season, I focused on other characters (Cordy, Willow, Oz, Spike). Still, there were a few moments where Buffy stood out for me. The first was in "Lie To Me", when Buffy confronted Ford and found out he was dying of cancer. She told him she felt sorry for him, and then threatened to kill him. The moment filled me with Buffy-love for the first time. The other moment was in "I Only Have Eyes for You". Buffy identifies: not with the (older) female victim of violence but with the (young) male perpetrator. Identifies, and is completely unforgiving. I was immediately intrigued by Buffy in a way that I hadn't been before. Both these moments have something in common: Buffy sympathizing/identifying with a violent young man, and still being ruthless and unforgiving towards him, not despite the identification and sympathy, but because of it. That's about the opposite of the usual assumption in fandom--usually, if you sympathize and/or identify with a character, the expectation is that you will be more forgiving of that character than of other characters.
I absolutely loved "Anne"--still my favorite season opener--but I ended up losing a lot of emotional investment not just in Buffy the character, but in the show as a whole during season three. Maybe I was getting tired of the high school setting. Maybe I had lost all patience with Buffy and Angel's romance. I liked Faith, but didn't really enjoy her storyline the first time I watched it. The show just seemed very static at this point. While I started enjoying it again in Season 4 (perhaps the least static season of them all), I wasn't particularly interested in Buffy as a character. I remember watching Angel season 1 and having a brief moment in "Sanctuary" where I thought that perhaps I didn't like even like Buffy at all--I think it was when she brought up her relationship with Riley when arguing with Angel. It seemed an immature move to me, and I was irritated. On the other hand, my sympathies with Faith were quite high at that point, and I was moved by Buffy coming to her aid on the rooftop despite Buffy's anger at Faith.
Season five of Buffy changed everything for me, because I am Spike fan and a Buffy/Spike shipper, and, like just about every Spuffy fan ever, I became a hardcore fan of his character, Buffy/Spike, and the show after watching "Fool for Love". I actually shipped them before that--I knew enough about the show to know that this was the season where Spike falls in love with Buffy. I had been trying to tell myself that I was merely curious about this relationship, but I had to admit that I already shipped them, and had since that moment in "Halloween" when Buffy is freed from the spell, declares "Hi, honey, I'm home!" and punches Spike in the face.
Now, Spike is another example of Buffy being unforgiving towards someone because she identifies with them. In "Becoming, Part 2" Buffy learns that Spike's reason for allying with her is that he wants his girlfriend Drusilla back. Her reaction is to call him pathetic, and tell him she hates him. "I lost a friend tonight!" she shouts, referring to Kendra, killed by Dru, and echoing Xander's earlier accusation that Buffy wanted to forget all about Jenny Calendar's death so that she could get Angel back (As a sidenote: poor Kendra. Her death is always overshadowed by other deaths). Buffy sees herself in Spike--in this case, the passion she has to suppress and the self-absorption she can't afford to give into if she wants to do her job as the slayer--and hates him for it.
Watching Season Five, I became quite taken with Spike as a character, and with the entire Buffy/Spike dynamic. I was definitely rooting for them to get together, which I felt a bit bad about because Buffy was so obviously opposed to the idea. But you ship what you ship. Adoring Spike also affected my view of Buffy--I could see the things he saw in her, her honor and her suppressed passion. (Not her kindness--I think souled Spike appreciated Buffy's kindness, but I do not think it was her kindness that soulless Spike originally fell for). I also really enjoyed the portrayal of her relationship with Dawn. For the first time, seeing her through Spike's eyes, she became one of my favorite characters.
I remember "The Weight of the World" being one episode where I connected with Buffy as a character in ways that were not Spike-related (I had no doubts, at this point, that I favored Spike). A Buffy who gave up for one moment and endlessly replayed that moment in her head was a Buffy I was interested in, a Buffy who saw giving up for one moment as killing her sister was a Buffy I cared about.
I was spoiled for a lot of things about season six. Quite a lot. The early seasons of Buffy were able to surprise me (I didn't know about Angel losing his soul, for example), but not season six. I was spoiled, really, for just about everything. This did not stop it from becoming one of my two favorite seasons (along with season 5--although I think I like season six better, because even though it has more flaws, it also gives me more to think about). I knew going into it that this was the season that turned a lot of Spike fans against Buffy. I knew that she beat him up in an alley, and fandom criticized Mutant Enemy for having gender double standards in their portrayal of domestic violence. I knew he tried to rape her later in the season, and then went and got a soul--possibly on purpose, possibly by accident.
I was even more determined than I had been before to like Buffy. In the first half of the season, this was a problem. I sympathized with depressed Buffy, but I didn't like her. I tried to like her, but I just couldn't see anything in her that I could connect with. I hit my low point with Buffy in "Gone"--I had a difficulty even sympathizing with her when she tried to make a social worker who was just doing her job think she was crazy. Worse, Buffy seemed to see the whole thing as nothing more than a joke. The thing I had always liked about Buffy was that even at her lowest, she was always focused on doing the right thing and being a good person. In this episode, she didn't even seem to care.
Fortunately, "Dead Things" is only two episodes after "Gone". In "Dead Things", I fell in love again--this time permanently, and more in love than I had ever been before. A Buffy who tried to turn herself into the police for accidentally killing someone, determined to do the right thing "for once", was a Buffy I could recognize. Buffy beating Spike up so brutally that he still had bruises in the next episode was horrifying, but still recognisably Buffy--the girl who was least forgiving towards those she identified with. Sometimes, if a character hurts one of my favorite characters, I will resent them on my favorite character's behalf, but other times, it has the opposite affect, and my appreciation of the character hurting my favorite goes up (see also: Angel smothering Wesley with a pillow). This time, my appreciation of Buffy went up. The key moment was, of course, the ending: Buffy bursting into tears upon finding out that it really is her doing all these things, expressing her guilt and horror at her attraction to the unrepentant Spike, and begging Tara not to forgive her. For the first time ever, I walked away from an episode with more positive feelings towards Buffy than Spike. I had lost a lot of sympathy for Spike after the balcony scene--probably it didn't help that that scene was one thing I had been unspoiled for, and if anything , I had been led to believe that Spike was entirely in the role of the victim at this time. I had been prepping myself for both the alley beating and the attempted rape, but Spike thoughtfully and deliberating trying to exacerbate Buffy's guilt and unhappiness so that she would be with him was not something I had been preparing myself to forgive.
From then on, Buffy remained one of my consistent favorites. When I went back and re-watched the first half of season six, I was able to appreciate her as a character instead of simply feeling sympathy and annoyance. I could see how her experiences had changed her from the person she was in season five, and appreciate the person she was the process of becoming, but also see the ways in which she was still the Buffy of the early seasons. In season seven, I found her one of the most enjoyable characters because I usually had to think about it for awhile in order to figure out what was going on inside of her head, but once I had done that thinking, she made perfect sense to me. When I later got a chance to read some of the original scripts online, I was pleased to see that some of my guesses of how she was thinking, particularly her thoughts and feelings about Spike, were more explicitly confirmed by deleted lines. By the end, I was definitely rooting for her, possibly above every other character on the show.
So that's the convoluted story of how I came to root for Buffy Summers.