With her lack of credit history, I’d definitely say take a look at Discover. My sons were able to get the Cap 1 Quicksilver card while they were in school but they both also had a Visa issued from their university credit union. I think Chase will want her to have a credit history for a least a year before they issue her a SW card.
It’s important for kids to get some credit on their own while in college. My DD19 also got a Visa last fall from her university. I’ll probably have her apply for another card sometime over the next year. It’s important when it comes to getting apartments, insurance and auto loans to have 2 lines of established credit.