In a lot of ways, non-profits and for-profit businesses are two very different things. When it comes to insurance, however, the two have quite a bit in common. 
Your non-profit's goals may be charitable, but you still must manage many of the same day-to-day risks as any company. Here's what you're going to need for starters:
- General Liability Insurance. This is the most important part of nearly any insurance package. General liability means that if something goes wrong, and you can be held responsible for it, you'll be covered. That means if someone gets hurt on your property, you won't have to pay for the damages out of pocket. This is of the utmost importance any time you are responsible for the physical space in which business is conducted.
- Property Insurance. It is difficult to run a non-profit without property or somewhere to conduct business. And you don't want to be left paying for damages yourself or out of the non-profit's funds.
- Workers Compensation Insurance. Laws and regulations regarding workers compensation may vary from one state to another, but generally you are expected to provide your workers with workers comp, even if you work with a lot of volunteers.
- D&O and Professional Liability Insurance. Directors & Officers insurance and professional liability can help to protect your non-profit against any concerns that arise in relation to your staff. You might not need D&O insurance just yet, as an unincorporated non-profit association might not have a board of directors in the first place. But a board of directors, and the D&O insurance to cover them, will be a necessity for becoming a non-profit corporation.
A non-profit may be focused less on making money than on making a difference, but that doesn't mean that it's not going to be run like a standard business in more ways than not. Ultimately, this means that you're going to be investing in a standard business insurance package.