They shouldn't charge VAT on a camera shipped to the US. UPS can charge brokerage fees for customs, so I'd avoid it. I've used regular mail for purchases from various European countries without difficulty. Once I sprang for DHL for an expensive camera from Slovenia, because it would have taken longer than I was comfortable with by regular airmail, and the cost of the shipping wasn't outrageous considering the cost of the camera, and I wanted reliable tracking. DHL is pretty widely available in Europe and many countries throughout the world. You can also get global FedEx.
I've made many international purchases, but mostly for used equipment, and I don't think I've ever been charged a customs fee. For a new camera coming directly from the country of origin, or from a manufacturer with a very aggressive US representative who wants to prevent third-country transactions, it is probably more likely that you will have to pay customs.