My position is a little different, but I can understand where your girlfriend is at. I would recommend doing what I did, but time is your biggest friend when it comes to building credit history more than what card you get. My big question is: does she really need a secured credit card instead of a traditional one? Probably not.
I left college without credit history and it was a bit of a challenge for me to rent apartments. I ended up paying huge deposits and fronting a lot of costs I didn't expect. I'm not a fan of financing things, but I was worried about my ability to eventually get a mortgage without credit history.
I tried applying for a normal credit card directly with a company because I liked the rewards, but I was rejected due to having no credit history (this is apparently pretty common). So I went to the bank where my checking account is held and told them I wanted a credit card. Since I'd been using their bank for almost 5 years, they seemed really happy to offer me a card and didn't require a secured account. The whole process took about 10 minutes and I got my card approved and shipped to me within about a week.
Because of my lack of history, my bank only offered me one card. It was a no-fee card that wasn't listed on their website. It's similar to their student credit card, and it only has a 1% cash back on everything and a very low limit, but it wasn't a "secured credit card" where they hold a deposit for it. I would avoid one of those secured cards if possible. It's a rumor, but I've heard they are not that good for building credit.
After about 6 months of buying all my groceries on the card and paying in full every month, I called and asked for a raise in my credit limit. This could hurt your credit score a little, but with no other debt, it might not matter much. It was no problem with the bank and required a single phone call. Now I'm using this card for all my normal expenses and trying to hold onto it for several years. Even if I get another card in the future, I will probably keep this card open to have a longer credit history.
Summary: Have her go directly to her bank and get a no-fee card; don't worry about rewards. Her bank will be the most willing to lend to her and they sometimes have credit cards they don't advertise on their websites. Avoid cards that require a deposit -- these are for people with bad credit who are known to not pay their loans, not people starting to build credit. Keep the account open and paid in full every month for several years.