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I would say wherever she banks and/or Discover. Discover tends to look favorably on thin files, has a student card option, has good customer service, and a free FICO score; on the other hand, going through whatever bank she has a checking/savings account with might streamline payment and account management somewhat, depending on how good their interface is.
I know that as a 19 year old I was grateful to have my first credit card be at the same bank as my checking account, since it meant everything was far easier to keep track of in one place with one online banking system, plus transfers to pay the bill went through nearly instantly. I know that's not necessarily the case with every bank, but the general point stands--for a teenager who's new to credit and looking to create a solid foundation, the most important thing is finding a credit card that's easy for her to manage well and consistently, and doesn't encourage her to overspend. Ideally that's something that can grow with her, doesn't have an annual fee to take into account, and has at least some rewards, but if you can only get one of those I'd say the easy management considerations are the most important.
I started at 18 with a student rewards card from my bank (Wells Fargo), and they gave me the best credit line I could get from anyone for nearly a year. She already has a couple of accounts so she's in a better position than I was, but I would recommend a card from whatever her bank or credit union is as a starting point, usually if you have a relationship with checkings/savings approval on credit products is easier.
After that I would also consider Capital One and Discover, as others have said. They were the next two finalncial institutions to approve me. With Capital One I got the Journey student card, which is a nice starting card as it has no annual fee and gives standard rewards. It started with just a $300 limit which was frustrating, but after their Credit Steps program (pay on time for 5 statements) it jumped up to $3,300, and a few months after that I got it product changed over to a Quicksilver so I still have a higher end card but keep the account history. Discover initially approved me for 1,000, it stayed at that for maybe 6 months or so and since then I've had consistent increases.
+1 Cap 1
My daughter opened a student account with Wells Fargo at 18 with no job and the automatically gave her a credit card with an $800 limit. She is now 24 and has built a nice credit profile. She messed up a bit on that student card but fortunately has learned her lessons and now has scores around 680-700.
jlynn0819
she plans to move out in about 6 months
I suppose she may be benefit from household income.