Technically you can't have your own credit card when less than 18 years old because until you reach age of majority, your signiture is not legally binding.
Most banks and credit unions also won't let a person under 18 open a checking account on their own name. I had to have a joint account with my Dad. The credit union at college bent some and allowed me to start an account when I started there, even though I still had two months left before turning 18--technically they were taking a chance in the name of customer service.
Steve