Question abt getting STD testing

I'm 18 years old and I am under my grandparents insurance. I'm not showing symptoms for any std, but I'd like to make sure that I'm healthy. should I visit my general doctor, obgyn or planned parenthood to get tested? I want to be safe and if something serious does come up I will let my family know but for now, I keep them on a need-to-know basis. Which option would have the least expensive copay and/or which would give me the best way to keep my family from finding out I'm getting tested?