DNA testing (sorry about the weird category choice)

Sorry if this is in a weird category, I have no clue where to put it exactly since its a bit weird for this app but it has to do with my dad's side of the family soo??? . . . Anyways. . . I look so completely white and European it's crazy. Most people question why I ever think about DNA testing because I can look in a mirror and say without a doubt I'm white as hell. But I've always been curious. My great grandmother had my grandpa when she was insanely young (11 or 12 is what I've been told) and the father was left as "unknown" on the birth certificate. And my dad was married before he met my mom and I don't know if he had any kids with her. He doesn't know either. He won't give me a name. She cheated on him and he holds a huge grudge against her and I honestly don't blame him for that. Has anyone done DNA testing before? What's the best place to use for it? I've wanted to find out my genealogy for as long as I knew this information but I don't really know how to go about it