You're in the US, me, in Canada. Although some differences, I am confident some similarities.
I carry 2 million $ general commercial liability insurance, and that is it. Errors and omissions insurance was very difficult for my agent to find, and once he did, very expensive, and not worth it.
I am not sure what the requirements are for legal issues but I would not even think about starting a training company without a substantial umbrella type insurance policy. I would contact someone at my states safety and health department or your local OSHA office and ask for some help.