I'll "black helmet reaction" myself by replying to my own post, but please also keep in mind what will be coming in your future. Do you have more kids that you'd like to help with college? Do you currently have an awesome credit score that will be hurt by co-signing your eldest's loans? Do you want to buy or build a better house? All of these things should be considered.
If you co-sign private student loans, you are 100% signing up to own the debt so far as credit rating companies and banks are concerned. Your debt-to-income ration will include those loans 100%, even though your daughter is the primary borrower. If you want to buy a new house or take out a home-equity line of credit to remodel or add on to your current house, you'll likely be offered higher interest rates due to higher debt-to-income ratio.
If you are confident that your family income will continue to grow, and that your daughter will be fiscally responsible while in college, you do one thing. If you think your daughter might see your financial contributions as guaranteed, do something different.
Financing college or any higher education has gotten way more complicated the past 30 years. UNL tuition increased from $72 to $155 a credit while I was a student, and then they added a per-credit surcharge of $50 per credit for business and engineering students a few years later.
Good luck.