Professional photographers should have insurance. The rates depend on several variables. I used State Farm because they offered a discount as they insured my home, cars, personal liability and other personal property. The insurance covered my equipment, any damage resulting from conducting business (someone trips over a light stand, etc) and liability and lawsuits. I was doing interiors photography so the worst case would be damaging an antique or original art work. My insurance agent spent an hour with me reviewing the policy options and how to minimize my liability exposure for each.
You should consult an attorney to decide if you want to operate as a sole proprietor, personal business or a singe member LLC. Your insurance rate could depend on which option you choose. If you purchase insurance directly, I would have an attorney explain what is excluded from coverage.
I set up a single member LLC to separate my family finances from my business activities. This was a simple, inexpensive (as low as $50) DYI process. One downside of an LLC is you must take care to avoid piercing the veil of liability protection. This means if you use a camera, lens, computer, etc. for both personal, non-business and for LLC activities, you have co-mingled your personal and business activities and the LLC no longer protects your personal assets from liability. You also have to keep a minimal amount of records about the business. This adds some level of cost. At the same time any capital equipment (cameras, lenses, computer, office furniture, etc ) you use solely for business purposes can be deducted from your taxes according to a depreciation schedule. Non-capital expenses are deductible as well.