Oh, lovely, I was searching exactly for a thread like that!
As already pointed out in her TV Tenure especially, the writers didn’t seem to be quite sure how she was or for that matter how close is to a regular human teenager (I mean it’s probably its own topic if Susan is a Teenager by Human years or more so one when viewed through her Gallifreyan Roots, which obviously weren’t even properly thought in those early Hartnell Years)
That being said… I think Susan is one of my favorite Companions, easily. Yes I’d agree that she really did got a poor hand with her televised run, but despite that I think even there are a lot of great bits, even if the “Grandfather” Scream can be a lot and yes has been overused in her TV Tenure.
That all being said, looking at all her TV Stories:
An Unearthly Child basically has Susan as its main focus in Episode 1, she is the big Mystery. And she gets easily some of her best moments here, you really get the feeling of watching somebody being a weird teenager, as @sircarolyn pointed out. For the rest of the Story she gets fine enough, but definitely is the least focused upon out of the main four leads.
The Daleks continues the streak of some great Character Bits with her. Her being the one to do that one task is a great Moment, and I absolutely adore the little Moment of her writing that letter and giggling at the Daleks for not getting names. It’s such a sweet moment.
With the Edge of Destruction, I think we just continue some rather out of this world portrayals of her. She is great in it and I do know Ian acts a bit strangely here too, but I think Carol Ann really went all out with a more alien Portrayal for her.
I am not going into the pure Historicals one by one, since I think those all suffer similarly from the lack of Susan and when she is there, she is just kinda there. Reign of Terror is the worst offender, some great Moments at the beginning, besides that? No. Similarly, as much as I do adore both Aztecs and Marco Polo, really you don’t get much out of those two, with the latter having a sweet friendship for Susan, but that’s about it.
Meanwhile, all if not most of the Sci-Fi Stories do her pretty much justice with a lot of great bits. The Sensorites and Dalek Invasion being pointed out makes sense, since those are easily the ones where she has the most focus given. Especially her relationship with the Sensorites, her making her own decisions here, how she talks about her home are all lovely Moments. Similarly, the Dalek Invasion has some great Moments with her.
While yes I do totally get why a lot of People have their troubles with her, many aspects of her don’t work too well in the televised run, there was often a big back and forth with how she should be portrayed due the fact, that it’s obvious that the People behind it didn’t know if the Doctor was from the future or was more of an alien. And I think Susan does suffer from it quite a bit, which is a shame, since I think Carol Ann is such a great Performer and does remarkable work with the Stuff she has been given to.
So I am really glad that she returned from BF and of course her Character being featured in other forms of Media. She is always a delight and I really adore how much energy she puts in those Companion Chronicles, giving just the right feel of Hartnell in them. (A bit off-topic I know, but I really wanted to mention it).
If we are also taking Expanded Media into account (like I did) Stories such as her Arc with 8 or Domain of the Voords are a great showcase for her and use her really well for the most part.
I am probably in a similar field as @sircarolyn, where my Idea of that Character isn’t exactly the one which was always portrayed on TV. But I overall really think she is a great Character and while yes you can’t really talk about her getting a proper arc in the show, there was often this feeling of finding a place for her to settle (especially enhance to some of her Audio Adventures), which is a nice theme for her to have.
In short: Big Fan, would love a return for her on TV someday!