If you have any interest in building your own bike, then a fixie would be a great first project. You should really consider asking a local bike shop about classes, or if any of their mechanics would be willing to teach you. You might find a passionate mechanic who would enjoy staying after hours and helping with a project.

If you do decide to buy a complete bike then I generally suggest going through a local shop. Local bike shops tend to cultivate local bike culture.

I say build. Built my first roadbike. It taught me a lot and I made friends.