I've discussed why I like this character here. We'll start with her first appearance:
Edge of Spider-Verse #2 (November 2014):
OK, as I've noted before, I've never read any Silver or Bronze Age Gwen Stacy stories, so I don't have the connection to the character that a comics just a few years older than I am might have. An older reader might say, "This isn't my Gwen Stacy!", but I won't have that.
The writer is Jason Latour. By and large, I have no beef with the writing. His dialogue occasionally smacks of "the way these kids talk today".
The art is by Robbi Rodriguez, with colors by Rico Renzi. The art is basically OK. Rodriguez does tend to draw George Stacy with a huge forehead, as though he were about to mutate into the Leader. I like Gwen's costume, similar to Pete's, but different enough that it has some originality to the look.
We're shown that Gwen is drummer for a rock band called the Mary Janes. MJ is the diva-ish lead singer/lead guitarist, an African-American girl called Glory (Grant?) is the keyboardist, and a dark-haired girl who is not named is the rhythm guitarist. They are seen practicing a song called "Face It, Tiger".
We get a flashback explaining some of Gwen's history: She was bitten by a radioactive spider, gained spider-powers, and became the entertainer "Spider-Woman". Peter Parker, wanting to become special like her, becomes the Lizard, and ends up dying in her arms. J. Jonah Jameson starts a campaign against Spider-Woman, accusing her of murdering Peter. Gwen feels responsible for Pete's death, but not in the way that Jonah means it.
Meanwhile, Captain Stacy is in charge of the police effort to catch her. The police are hot on her trail. We cut to Matt Murdock - who on this Earth is a crooked lawyer working for the Kingpin, which I thought was an interesting twist - having lunch with a muscular, grey-skinned comedy Russian called Aleksei (This world's version of the Rhino?), and sending him knock off George Stacy, in hopes of winning over Spider-Woman.
Aleksei attacks George at a Mary Janes concert, which Gwen is late for. She beats up the somewhat confused Aleksei, but George gets the drop on her. She unmasks, and explains to him why she became Spider-Woman. He weakens, and lets her go. All this is observed by the British Spider-Man, leading into the Spider-Verse storyline.
Overall: An interesting first look at the character. She would play a fair part in the Spider-Verse story, but I'm not going to get into that here, as I hope to give that story its own thread at some point.