Advice on finding my biological paternal grandparents

My father was adopted but never cared to find his parents. I want to find out who my biological grandparents are mostly for health issues but don't know where to start and feel it would be harder than normal due to the circumstances My biological father was adopted by my grandparents in the 60's. When my mom was pregnant with me she asked my grandmother if there were any health issues to be aware of and other than reassuring my mom there weren't any issues the matter was dropped. My mom and my self occasionally asked my grandfather and step grandmother but always got an answer like "we'll tell you when you're older/later". I went to visit my grandfather this past weekend and asked again, the answer I got was anti climatic and the 30 years of secrecy doesn't make sense. Apparently my grandmother couldn't concieve after their first kid so a doctor friend of theirs matched them with a girl who didn't want her kid. I feel like there's more to the story and now I'm curious as well as want to make sure there aren't any health issues to keep an eye on. My dad apparently doesn't care who his parents are so no leads there. It's also bee 15 years since I've spoken to him, and he hates my grandfather for dumb reasons so my dad won't be any help and after this past weekend I don't think my grandfather/step-grandmother will be of any help. Does anyone have any advice? I was thinking of starting with 23 and Me or maybe ancestry.com could have some leads but I don't know where to start