Welcome!
I don't have much in the way of firm likes as they tend to shift by mood and what I like are the character interactions which makes it hard for me to say "THAT character is my favorite."
I will say that I have seen many good things about Cordelia even in season 1, even if she was greatly flawed (however, I'm not going to sympathize with her over Willow tricking her into deleting her work, Cordy had that coming, and Cordy probably grudgingly respected Willow on some level for doing that), and it really shows in season 3 Buffy where she, despite her conflict with Buffy, actually stands up to Gorch, saving Buffy. I've always found it touching that Cordy was remarkably forgiving (I don't personally know of any females who pride themselves on being a bitch who'd let a girl out of a cage after a mere talk about the ethics of boyfriend stealing), and though she was again not all that fond of Buffy, in Helpless she not only takes a jock (I think) to task for pushing Buffy down, but momentarily drops that dumb girl act when Buffy tearfully asks for a ride and says, with concern in her voice, "Of course."
She is also a strong character (strong should not be confused with invulnerable or super powered), and when I first watched Buffy I really found it useful to see a show of women being feminine while still being strong and assertive. Cordelia was one of many characters that fit the bill.
Perhaps notable, I'm one of the defenders of Xander on this site, though he's flawed (as all the characters are, which is part of why I love them). I probably wouldn't, but he gets way more hate than he deserves, IMO, often by twisting the actual canon to justify it. If it wasn't so over the top then I'd probably criticize him more myself. 😉 (I'd probably defend Dawn and Connor the same way, but thankfully enough others do that for me, and they surprisingly don't receive the same amount of hostility.)
I can say that now that I'm older that I saw the characters a bit differently on a rewatch, but I don't feel like going into that here. I will say that on my first rewatch that Willow wasn't the sweet angel I remembered, and Xander contributed a lot more and saved the day more often than I recalled from the first viewing. On a rewatch a few years ago I noticed that Buffy was a lot ruder to her mother more than I remember and Joyce, flawed as she was, showed the patience of a saint at times with Buffy's attitude (I'd have gotten slapped or worse, and come to think I deserved it, if I said some of the things she did to authority figures). I give Buffy a pass though because it's obvious she loves her mother about more than anything, and I also make allowances for age.
Perhaps--I emphasize perhaps--my favorite is Giles. He's actually shown up in my dreams as a father figure (in one dream I was a kid again who left Dad to go home with Giles, my real dad). But as a lover of horror and people overcoming tragedy, I could've handled him dying or, even more horrifically, being turned into a vampire who antagonized the rest of the cast in brutal ways (I'd even prefer that to his leaving in season 6).
I am not a particular fan of any ships. I can appreciate Tillow for helping to make such relationships acceptable to the mainstream and showing it in a tasteful rather than titillating or freaky way (or done strictly for laughs), but overall I'm more about the story, which ships can enhance but don't interest me in of themselves. How insanely jealous all the characters get does get on my nerves at times (it wouldn't bother me if one or two characters were that way, but it seems everyone regresses this way).
I'm not a fan of seasons 6 and 7 of Buffy (a few awesome eps in those seasons not withstanding), but this doesn't mean I'm against dark or realistic (see my idea of how I wouldn't mind Giles being a vampire, and I think season 2 and 5 did dark a lot better anyway--since I don't consider season 6 that realistic I'm gonna say season 5 did realistic better as well). But I do love season 1 and like season 4 more than most do. Seasons 2 and 3 are my favorite, and 5 used to be but the flaws slowly came to be a bit too much for me over time. As for Angel...that's hard to say, I pretty much liked it all (even season 4), but it seemed to me that they all had moments that it dragged on a bit much while also having moments of pure awesomeness (that depend on the other moments I find harder to sit through to actually make them awesome). Offhand I can't pick a season and say that's my favorite, and now I'm tired of sharing.
