Magazine Scam, Help?! I need to know who these people are… will contact for legal action.?

I recieved a call last night from an unknown company . They said I was a runner up for winning a contest (I have entered a few contests lately) and was going to be sent a diamond watch, as well as 2 years of free magazine subscriptions. They proceeded to tell me that I would be charged nothing for the watch and the subscriptions, but that I would be signed up for two other subscriptions of my choice for around 3 dollars a week. To verify that I was the right person, they asked for the rest of my debit card info. They already knew my address, home phone, cell phone, card type and first few digits of the card…so it sounded legitimate. You don’t have to tell me what an idiot I was for doing that, I know it. I reported my account as compromised once I had gotten off the phone. They had already charged $50 dollars to my account, which I am disputing. I called the attorney general to report it as a scam, cannot contact the company themselves due to blocked numbers.Anyone have conact info?
I believe the name of the company may be Big Sky Publications.

Since the charges have not completely cleared my account I do not know, they were simply listed as "Periodicals" on the charge statement.
Note: They will start sending me periodicals soon, expecting me to pay for them, though I did NOT authorize them to use my debit card info. to pay for this. I am considering putting a fraud alert on my credit report to disable them from affecting it. Anything they send will be returned, I do NOT want it!
I never agreed to pay them a dime. They said they would send paperwork in the mail before anything happened. I did not authorize the use of that card for any such purchase.
They just called under the name of US Magazine Service, claiming that because I gave them my information, I had agreed to pay. They refused to give me any contact information. No phone number, no address, nothing.
After filing a complaint with the BBB less than an hour ago, the BBB website led me to a genuine contact number. I called and stated that I was calling to cancel my subscription (federal law states that all phone transactions have a 3 day cooling off period, even if I hadn’t been scammed) the woman told me my subscription had been cancelled, and I would recieve one more phone call from the company to be recorded that I had cancelled. Should I also send an over-night cancellation letter to be sure there is NO question that I cancelled my "subscription" ?

Try the local police and BBB