Those are some great posts by Kevin Ross!
When you say agency nurse, are you talking about local registry work? If so, while I hate to discourage budding entrepreneurs, I think it will be almost impossible to break in that market with you as your sole product. A hospital hires a registry with the reasonable expectation of getting a good portion of their needs met in many departments (specialties). You just can't do that alone.
If you are talking about travel contracts, that is a different kettle of fish altogether. I've been traveling since 1995, and formed my own agency in 2004 and have been working for myself ever since. On business form, I started as a sole proprietor, and a year later decided in favor of a C corporation (an unusual choice, most do LLC or S corp). But as Kevin says, there are many places to learn about business types, including any book on starting a business. I agree completely that you need to have your own business to properly represent yourself.
One small difference with Kevin's info, I invoice weekly, and I've not heard of any travel company doing differently. Cash flow and financing a payroll are big issues when you are paying employees (of course your situation is not that, but that is still the expectation - heed Kevin's advice about thinking like a business, not as an employee). Standard business practice is that invoiced businesses have 30 days to pay. This means a minimum float of 5 weeks before you get paid. While it takes almost no money up front to start your own agency, you do have to be prepared to have significant savings or line of credit to afford this lag time. That financial advice applies to regular travelers as well, as anything can happen while away from home.