Basic Errors and Omissions insurance should cover what your describing. There could be local/state laws concerning running the vehicle for prolonged periods of time, a call to your state department of permits should give you a solid answer to that.
When I started by business off of a franchise model, I had the same questions. At the very least I would make sure you have a general liability policy. There are probably not a lot of risks involved with your business, but if somebody trips and falls getting in or out of your air conditioned van and gets injured, they may expect you to pay their medical bills. It's good to be covered for this.
You can shop around for a good rate from any number of reputable insurance companies. Just search for "business liability insurance" in your city. Above all, talk to an attorney. It will be worth the time and money in the long run. If you know your business idea is validated and will work, if you are going to the lengths of creating a business plan and marketing plan, then you should be talking to an attorney. At the very most you'll probably be paying for an hour or two of their time at the most.
Actually, since your doing a form of possible ride sharing you might be subject to the beefy insurance regulations found here
If you need that policy, it starts at 50k!
Local transport companies are subject to different regulations but are required to carry by law in CA:
Work comp for driver
Vehicle insurance including liability, accident, and possibly physical damage.
I can help for a reduced fee if you have additional questions on this topic as we are also compensated by the insurance companies for the policy placement.