I would avoid Capital One and Discover at all costs…
If your parents have an American Express card, have them make you an "Authorized User" on their account. Even if they don't actually want to give you the physical card, being on their account will establish you history.
Next step, I would wait 6 months and then apply for a "Secured" Visa card from your bank.
I'm turning 21 next month, with 750 FICOs across the board. Did the above, spent wisely, and I've managed to churn over 400,000 miles this year.