I'm trying to determine whether my teenage daughter should receive the HPV vaccine to help prevent cervical cancer. Since it's a new vaccine, I'm concerned about the safety of it. What risks should I be aware of?

VERY safe vaccines. As safe or safer profile than any other vaccine you give your kids. Nothing differed from placebo in initial studies of over 30, 000 men and women other than pain, edema, red an itching at injection site, and fever, nausea, headache and dizziness. That is it! most common 'severe' reaction is headache. 100 million doses distributed worldwide now with great safety data since release as well.
Very safe. The media has made this seem like a controversial vaccine. The safety profile is very well studied and clear. The most common side effects are pain at the injection site & fainting in the first few min after injection. The "shell" of the vaccine is the same as the hep b vaccine which has been around for over 40 years. 70-80% will contract hpv over their lifetime.
Safe. Studies show that when HPV vaccine is given to women who have never been exposed to the HPV virus, they were nearly completely protected against the HPV Genotypes 16 and 18 which are responsible for 80% of cervical cancers worldwide. The protection lasted up to 8.5 years. **Gardasil also protects against genital/anal warts and protects against cancers of the vagina,vulva,throat,tongue and anus.