Your final decision as to the legalities and insurances for your freelance business should be based on professional advice from lawyers and insurance agents or brokers. If you wish to research the options to start with, The Professiona Photograher of America (P.P.of A) and the America Society of Media Photograher (ASMP) are recommended. Their offerings and recommendations are specifically intended for photographers. Consider the insurance programmes that come with membership.
Of course, laws and regulations can differ in various jurisdictions and circumstances so seeking professional advice in your location is important
I can tell you what insurances I carry to give you some ideas of what you may require.
PUBLIC LIABILITY- This covers you for any accidental damages you cause to people or property, in the course of doing your work, on your premises or on location. If someone trips and falls on an electrical cable or light stand, if a hot lig burns a hole in somethg, etc., etc.
NON PERFMANCE- For example- if a job is time sensative- the client has paid to reserve advertising space and you miss the deadline. You shoot an event that can not be restaged and for whatever reason, you can not deliver the images, etc, etc. Circumstances like these can lead to a lawsuit.
EQUIPMENT- A comprehensive policy to cover the replacement of lost, or damaged equipment due to fire, theft water damage, in yor home, studio and/or motor vehicle. I make certain the values set are current replacement costs.
It is important to consult a lawyer to assist you in designing a contract form. Your contract can set out the certain limitations of liability and what yo guarantee and what you disclaim. These clauses can help determine the extent of your required insurance coverages. How you register yo business- as a single proprietorship, corporation, etc., also affects liability issues- your lawyer can explain the details, advantages and taxation issues.
You mention that you ordinarily do not do photography for money. Once you accept payment you are representing yourself as a professional. Make sure the fees you receive will cover your overhead costs, insurance is only one of them.
Some of this may sound onerous and a bit scary, but settg up all of this in advance will avoid regrets in the future.
Good luck- much success