Credit cards are issued by your bank, you pay one yearly fee, 175DKK around 30USD. More often than not the bank will give you a VISA debit card for free, or a Master Card with 30.000DKK limit, no interest if you pay the debt of each month (The bank will do the transfer from your account for free, assuming that you have the money of cause).
Paying bills online: Free Domestic bank transfer: Free Credit card / debit card: Free or fixed fee Getting a check made out: Pretty expensive