Any US employer can sponsor you to work in the United States. In most situations, the sponsor must be an existing and independent US employer – one that you do not own the majority of. There is no requirement that the employer be of a particular size or in a particular field. Individuals cannot sponsor you for a work visa.
The visa category will likely determine the documentation and evidence required by the US employer sponsor. With E-3 visas, the employer will be required to have someone in the company act as the signatory on legal documents related to your sponsorship. The employer will also have their business verified by the US Department of Labor as well as receive a certified Labor Condition Application.