I would say it depends on several things. My wife has been an AU on my amex's for about 2 years, but I figured it was time to start building her credit up. I really did not want to get her a capital one card (I didnt want her stuck with an ultra low CL for her first card) and I tried the preapproval site for discover and got the who congrats you've been pre-approved for blah blah blah... I app'd for it and she got denied... I guess they found out she has no credit history after all. I then remembered that she has had a wells fargo savings account for quite some time with a decent amount in it. Figured it would be a good bet to try that as they can see she has assets. App'd and she got approved for a wells fargo platinum. Nothing exciting but they gave her a $1,500 CL for her first credit card ever with absolutely no credit history other than being an AU on my amex. My point is, really check your options before settling for anything that might not be great.
What does her report look like now? Any history? Loans? Late payments on anything? All of these factors will weigh heavily on her options!
How about adding her as an AU on some of your cards first? If not then id say try for like 3 different cards if all denied go with a secured card. For the secured route id go BofA. For unsecured try like chase or discover and a CU if you guys belong to one. Good luck and let us know the outcome
Does she have anything in any banks that could help gain her some leverage? If she has a checking account in a bank, ask her to talk to someone in the bank to see if she qualifies for one of their cards. If not, you could try capital one's pre qualification site to see if and what she would qualify for
If she's a student, apply for student cards. If not, I would go to your local bank/credit union and see if she can qualify for anything with no history. Otherwise, you might have to get a Cap 1 card. There's no need to worry about the interest rate if you pay in full every month.