If the bank account is to be carried on under the Business Name, the bank will want to see the Business Name registration certificate. You may also decide to take out some insurances. A first priority would be Public Liability insurance. This would cover you against any accidents to customers while they are on the premises. Another policy would be personal accident and sickness for yourself.
Most professionals now take out professional indemnity insurance.
You would be well advised to take out private superannuation. You may require a licence or practising certificate to carry on your trade or profession. Now for equipment needed. At the present day, most businesses will have the following. You will need a computer system.