You will need a bank account. There are many accounts specifically for young people, shop around and see what they are offering and best suits you. For lots of useful information on choosing the right bank account click here.
Third Party Access allows your parents to have access to your bank account - they can check your balance, transfer funds, pay bills etc. The account and the money is still yours but your parents can help you to manage the account. To set this up contact your account provider and request a third-party mandate arrangement.