To the OP: your parents are wise. My first fixie had hand brakes (and still does), and I was still freaking out for about a week, with old habits that die hard (e.g., the impulse to coast). For me it was a strange transition, so having the hand brakes gave me incredible peace of mind. This fixie is still the bike I use when I know I'll have unavoidable hilly terrain. It wasn't until a few months had passed that I felt secure enough to go brakeless, and that included a buffer month just to be sure I wasn't jumping into it too soon.

Oh, and to the poster who finds brakeless riders over 30 a rarity: I didn't start riding fixed until I was 41; brakeless a few months later. I feel safer amongst older brakeless fixed gear riders, since we tend to feel our mortality more and have a greater respect for it, and we don't try reckless stunts to earn street cred.