Q: I entered my gift card number...but it asks for visa, mastercard, discover, etc. what do i choose

The article you referenced, HT1574 gives detailed instructions on redeeming gift cards.  It is not like a credit card.  You redeem a card for $10.00, it puts a balance of $10.00 on your itunes.  Any purchases you make are deducted from that balance.

HTH

It shouldn't be asking you for another paymnent method, unless it is just trying to verify the account (security feature).  Try editing your payment method to None, then choose done. 

If that fails, you may need to contact iTunes Store support.  They can look at your account, and maybe provide better advice.

http://www.apple.com/lae/support/itunes/contact/.

Good Luck.