Can I recommend my story? Lolol. Mine has the tropes you mention, surviving in the modern world etc, learning about her world with some domestic fluff. However it takes a serious dark turn after that so be warned.
It's called Binded, rated MA.
Here's the summary: Kagome, now a modern-day miko, discovers Sesshoumaru's spirit during an exorcism. Desperate for answers to her inconclusive past, she resurrects and binds herself to him—a decision that inevitably leads to catastrophic consequences. Domestic fluff that slips into the dark. [COMPLETE]
Hope you try it out!