Ubank have a good online account. Can have a transaction account linked to debit card and a high interest savings account. Can also set an auto sweep up to keep anything above a specified limit in the savings. Think savings rate is 2.55% at the moment as long as you deposit $500 each month
Account has to be in personal rather than pay Ltd name but most people are sole traders so that is fine
Just use a normal account for Uber, it’s the same as a business account in all but name. Suncorp bank has a free transaction account. ING and BankWest are also good options. Up bank is awesome for getting an account up and running right away, up.com.au this would be my choice.