Bearing in mind that I live in Australia, only one major overseas payer needs invoices from me. I just buy an invoice book from stationery shop. My invoices work fine for the past 5 years.
Also consider about the tax factor too. The side income from photography would push you into a higher tax bracket when the business starts kicking in.
One thing good about earning an income from photography is that you could offset any spending on it against income in tax e.g lenses, camera, computer etc. So far the taxman hasn't questioned my claims for reduction.
you have to decide the scale and scope of photography business you intend to do, then decide on the desirability of registering a business. to avoid hassles, a sole proprietorship will do. less paperwork, less fees to pay, less associated costs of running it.