Credit Card for my college student

My soon to be 20 year-old daughter, sophomore in college, would like to apply for a credit card. For the past year, she has used a secured Visa card through her bank. She always pays her card in full and on time, yet it only gives her a credit score of 682. She has worked since she was 16 years old; always works on breaks from school and has almost $7K saved in her bank account (she has paid some of her college expenses; buys her own clothes, pays for car insurance, (she doesn’t own her own car), etc.) and she’s a very responsible person. There are so many credit cards out there, what if she applies and is rejected? Is it wise to get a Costco card with a CitiCard (even though there isn’t a Costco near school)? I’m a single mom. I don’t know the best advice for her. Thank you!