Thinking about starting the process of converting

I have been interested in becoming religious for 3+ years now and I have spent a lot of time reading about and researching various faiths, and more recently I have become fascinated by Jewish culture, history and, traditions. I am giving serious thought into conversion but I am worried that since I have no Jewish heritage or religious experience at all (my family and grandparents on both sides are all atheist) that I won’t be accepted. Is this a reasonable worry or is it for nothing? I’m also scared to tell my family about my interest in converting because I heavily doubt that they would understand and that I don’t see religion the same way they do. How could I try to explain it to them?