An OBGYN is the specialist to go to if you are looking for the Gardasil vaccination. Gardasil protects against the most high risk types of HPV, a virus which causes most cases of cervical cancer. To date, it is recommended that both boys and girls get this vaccination by age 11. There are certain caveats to getting the vaccination though; for instance, insurance providers only cover the costs of the 3 injections if you are at or below the age of 26. If you are over the age of 26, consult an OBGYN for more information about the vaccination. OBGYNs also administer pap smears and HPV co-testing, which is a way to screen for cervical cancers, and should be a routine part of your gynecologic healthcare regardless of whether you have received the Gardasil vaccination or not.
Regarding breast cancer; mammograms screen for breast cancer, but any physician (family care, internal or general practitioner) can give you a referral to get one. Mammograms are recommended at or over the age of 40 on a yearly basis unless of you have certain risk factors in your medical of family history that change the recommendation to start mammograms at an earlier age (usually 35).
Treating cancer requires further physician specialization. Breast Cancers are treated by Oncologists while gynecologic cancers are treated by Gynecologic Oncologists. I would recommend establishing care with an OBGYN to discuss each of your questions in further detail.