The first student loan that she should take out is a Stafford subsidized loan. This is the cheapest loan out there (except Perkins which you have to have a very low income to get). Get in touch with her financial aid office to find out the preferred lenders, but this is an easy loan to get which will not require a co-signer (not a credit based loan). Once she has maxed out that loan, if she needs more, she should get a Stafford unsubsidized loan. There are limits on the Stafford loans, but I can't remember what they are for undergrad (and I think the max just went up).
The reason you should do the Stafford loans first is because their government backing means that there are more and better protections for the borrowers.
If she has maxed out these loans (and check with the financial aid office to make sure you're all on the same page), then you're in the realm of private loans which are credit based. She should first apply on her own. The company will let you know if she needs a cosigner after she applies.
A note on schools' preferred lenders: the NY Attorney General just got settlements from a number of NY colleges and universities that received kickbacks from their preferred lenders (as well as preferred lenders in other states). Very often there were benefits for the students in using the preferred lenders, but not always. In my extensive taking-out-student-loan experience, the preferred lenders are easier to deal with because they often have internal systems at the school, and often have a number of perks--like reduced interest rates after 24 on time payments, reduced interest rates for automatic payments, etc. For me, the preferred lender at my schools was a good deal for me.
Student loan companies are a business, and they hope that you don't know all of your options. I would be wary of student loan companies that want to start with you cosigning a loan. While there is sometimes some benefit to keeping all of your loans in the same place, that should not be the reason that you select a loan company for your daughter's loans. And it seems to me that you're starting at the more expensive end of your options.
Lots of folks on these boards knock Sallie Mae. I think Sallie Mae is really still the best place to originate your loans--and frankly, the folks who complain about Sallie Mae are folks that have had trouble paying Sallie Mae. If you stay current, and let them know before you miss a payment, they will go the extra mile to help you out. And the Stafford loans are being offered by fewer and fewer lenders with this current financial crunch, but these kinds of loans are SM's bread and butter.
