how much liability insurance is needed to open martial arts school

I am not from your state and do not purport to give legal advice there, nor should this answer be considered a contract of legal representation.

In all events you should have some type of general or public liability insurance. This is true whether you operate as a propritetorship. LLC, corporation or partnership. The premium will depend on underwriting guidelines of the insurer for your type of business and the particular premises.

A "waiver" as you call it, is of limited value although many states allow some limitation of liability by statute or by contract, depending on the particular activity. It may also depend on using very particular wording in a document or on a posted sign.

Even still, there are visitors and third parties who may not be covered by a "hold harmless" or "indemnification" agreement or posting.

In conclusion, there may be ways in addition to commercial insurance to limit your liability, but this should be taken up with both a good local insurance agent and a local lawyer, for insurance and legal advice, respectively. In any event, you should not "go bare" or self insure, unless you are prepared for defending your self in a possible lawsuit and paying any judgment which might be entered against you.