This will help you keep the accounting clean to prevent issues with taxes and help make your business more professional. Typically, you will need to have documents like your Employer Identification Number (EIN), business formation documents, ownership agreements, and your business license to open accounts.
Learn more on the SBA’s guide here: https://www.sba.gov/business-guide/launch-your-business/open-business-bank-account
You will want (or may be required to get) a combination of insurance coverage. There will be the typical types of insurance any business would need like worker’s compensation, unemployment insurance, disability insurance, etc. Learn more on the Small Business Administration’s website.
Specific to aviation, you will want to secure commercial insurance that includes things like liability and property protection. The key here is that it needs to include aviation in the coverage as many “normal” policies will exclude aviation – clearly not something that will work for your flight school. Additionally, you will need commercial policies on your aircraft that provide coverage for instruction, rentals, and any other types of flying service that you plan to provide. While your commercial policy will likely have a provision to cover your instructors and customers, it is wise to help mitigate risk and better protect your employees and customers by having them also purchase their own CFI and Renter’s policies which will protect them specifically. Many aviation insurance companies offer special deals to schools on CFI and Renter policies. You can contact them for more help and guidance specific to your school. Assured Partners Aerospace (https://www.assuredpartners.com/aerospace/) has worked with AOPA for a long time and has an experienced team of brokers that can guide and help you shop for a good deal on commercial insurance.