The basic comprehensive test only checks for Gonorrhea, Chlamydia since these are the most common STIs. Some also check for Syphillis but when you go in, ask for:
Gonorrhea, Chlamydia, Syphillis, Herpes Specific Test, HIV. Of course you know about the HPV Test but during your next pap they can do that for you as well as check the outside surface for any warts.Your insurance should cover it because the new pap smears (ex Thin Prep) look for abnormal cell tissue growth from some HPV strains.
If there are any other questions, just ask away. We are all here to help