First credit card question: How long after your purchase does it take to get billed the min. monthly payment?
I made my first purchase a few days ago, and, currently my minimum payment (due at the beginning of July) is $0. Does this mean that I won’t be billed for this purchase until next month? Also, if I do pay some money this month (even though the minimum is zero), will that still go toward my credit card balance?

Read the small print on the letter that came with your credit card. It should say how much of a grace period you should have before you have to pay. It might be about a month. But it depends on when the period started, probably around the beginning of the month.
Your charge should show up soon on your record. Basically, any money you send to the company that’s attached to your card will show up in your account.
Have you received a statement yet?
oh yea it will still go toward your balance. if its your first credit card and first payment i think you should pay atleast what you feel is right, just to be on the safe side..