Good on you for getting your own account and taking control! As if this needs saying, do not ever give either parent access to your new account.

It sounds like your parents really dropped the ball on teaching you to manage money, and I'm sorry for that. Most adults maintain both a checking and a savings account, so that the bulk of their money is in savings and therefore safer. If you haven't already, I'd recommend getting a low-limit credit card and practicing making small purchases and immediately paying them off. That way, when you're ready to make a large purchase, you'll have a credit score.