Create a NEW account using these instructions. Make sure you follow the instructions. Many do not and if you do not you will not get the None option. You must use an email address that you have not used with Apple before.
I had this exact same problem with the new iPhone I bought on 1/4/13. The walk through they provide on how to do this is useless because it fails to explain that if you are already having the problem of not getting the "None" payment option with an Apple ID then you will need to create a completely new Apple ID.
I had to do this 7 times when I bought my iPhone to figure out how to finally be able to use the Home Sharing option in iTunes to put my music collection on my brand new $500.00 iPhone. Pretty pathetic if you ask me, but since it made me so angry I want to make sure other know how to do this so you don't get as upset as I did.
#1 If your current or soon to be "old" Apple ID is not providing the option for "None" as a payment option then you need to make a brand new one.
#2 IMPORTANT STEP!! - You will need to use an email address that has not already been used for anything related to a previous Apple ID. You might need to make a brand new email address. I had to do this 6 times before I realized that you have to create an Apple ID through iTunes or it won’t give you the None payment option. It won’t work if you are just creating it through one of the several other methods to make an Apple ID.
You must make your Apple ID through iTunes, or the None payment option will not be available. Also the email address you use while creating it cannot be used with a pre-existing, or previous Apple ID.
#3 Open iTunes, then open iTunes Store (upper right corner of iTunes).
#4 Click on App Store (upper center of screen).
#5 Scroll down the screen page until you see Top Free Apps on the right side.
#6 Choose any one of the FREE apps.
#7 You should either get the option to create a new Apple ID in a pop up window/box, either that, or it will pop up with some kind of disclaimer and then it does the create new Apple ID.
Either way just create a new Apple ID when it gives you the option to and then when you get to the page that looks like the payment page the "None" payment option will finally be available.
Note: You will still have to fill out the information on the payment page. As long as you choose the "None" option it will not request any credit card information.
#8 You will be sent a confirmation email to the new email account. Just follow through with whatever it tells you and viola now you can use your Apple Device.
What a pain in the keester, eh?