Jelissa is a warrior, recently arrived in Skyrim from Cyrodiil, aspiring new member of the Companions, just found out she's Dragonborn. She's now in Markarth to find her roots - her mother grew up here, but left the city in the aftermath of the Markarth Incident. (There's actually more to it than that, but those are things Jelissa's yet not aware of, so she can't take them into consideration.)
She has met Bothela and Muiri, and learned that Bothela is her mother's aunt, that Muiri is her cousin, and that she has another relative, Bothela's nephew, her mother's brother, in Cidhna Mine, imprisoned for being a Forsworn.
She's also learned that Bothela isn't too fond of the Forsworn, she thinks they bring nothing but trouble, and that the Silver-Bloods shake the old lady down for money every now and then. Most people she's talked to seem to dislike the Forsworn.
On her way to Markarth, she was attacked by Forsworn, so she's not thinking very highly of them herself.
Jelissa is a helpful and righteous young woman who's eager to prove her worth, and she also feels a sort of loyalty to the Markarth since it's the only place in Tamriel where she has relatives, as far as she knows.
When it comes to the Civil War, she hasn't chosen sides, but she really hates the Thalmor (something her mother taught her). She's recently began to feel a connection with Talos, and she's slowly beginning to feel sympathy for the rebels. She's Breton, but feels a connection to Skyrim and the Nords as well. The Jarl of Markarth is on the Empire's side, but he was also involved in the Markarth Incident, which, as far as she knows, caused her mother to leave Skyrim, and lead to the deaths of lots of Reachmen, her own kin.
And now she has this note about meeting Eltrys in the Shrine of Talos, apparently to discuss the murder they witnessed in the marketplace. What should she do? Get involved? Side with the bloodthirsty Madanach? Help the corrupted Silver-Bloods? Or just stay out of it?
Input please!