The Basic Riders Safety Course (MSF) is one of the best ways to become acquainted with riding. You can watch videos and really "see" what it's like to be "unseen" on the road. Trust me... you must ALWAYS have a Plan B. Not to mention that you develop a VERY keen sense of surroundings by riding.
[an aside]In the last year I picked up running as a hobby, and I am just as unseen running in a yellow vest as I am on a bike even with the highbeam on. If it wasn't for my "6th sense", I can promise you that I would have been hit by a car by now.[/aside]
You've clearly brought up some common parental concerns. If you remind your parents that they can probably list just as many people that got hurt driving/riding in a car, you might be able to point out that any activity that involves leaving the house also involves some risk. Tell them you want to do everything in your power to reduce those risks, and that you want to go about this the safe route. Remind them that you want to buy LOTS of safety gear (Helmet, jacket (if not pants), gloves, boots) and that you are doing research on the topic.