This is what I've thought of so far. I however don't have much experience with budget rig gaming.
She does not need an OS, Mouse, keyboard, or HDD. She needs all the other items though. She has a budget of exactly $500 and will spend no more.
She wants 1080p.
Plays very few games. At the moment only Skyrim, Portal 2, and A Ticket to Ride. She's states she'd be willing to expand if her current computer didn't suck.
Buying from US retailers.
If it's in the part picker list, she needs it.
http://pcpartpicker.com/p/29e1A
Thank you for your time and input.