I am self-employed and want to get health insurance.  What is a good
way to do so simply and affordably?

I am male, 23, non-smoker, no history of health problems.  I don't
care much about the size of my co-pay for small expenses (e.g.
check-ups, small prescriptions).  I do, however, want to be completely
covered in case I need a costly procedure.  I live in Los Angeles.

The simple rule is the higher the deductible, the lower the premiums.
If you can find the correct insurance agent, that person can usually
give you some good recommendations. Alas, I can't tell you how to find
that person. I know one, but he is retired in Illinois.