I was in a similar situation a year ago. Had the same "follow the rules" arguments with my parents. For the first few months after school I found contract jobs, which payed well enough, and left me plenty of time for my own thing and reflection. I highly recommend this path if you can stand living on the cheap and not knowing when your next job will surface.

After a few contracts I wound up joining a cool startup as lead developer since I wanted to pay off student debt fast and get some experience before starting my own. In a year or two, I'll likely be finishing up with this startup I'm at now and will have saved enough money to pursue my own thing full time for a while. Who knows what will happen then ...

This all from someone who had some student loans to pay off and not much money saved.

Both contract jobs and longer term employment with a startup have been hugely valuable experiences that I am grateful to have had before starting my own. There is a huge continuum between working for a fortune 500 company and as an entrepreneur.