Different regions have different valid payment methods. Refer to: Payment methods that you can use with your Apple Account - Apple Support Note that these are ones that are accepted, but specific kinds (e.g., credit or debit cards) might be required in particular circumstances. I know that account balance alone may not be accepted for some things in the USA. The article would be better titled "might be able to use".
Just in case you happen to not be in the USA (the numbers provided previously are for the USA), here are some ways to contact Apple in other countries too:
It won't let you select the gift card because the gift card isn't in there. Once you redeem it, it turns into account balance and the card itself no longer has any value. Account balance is always at the top of the payment method list and is always tried first unless what you are purchasing required a different kind of payment method. For more information see How apps, content, and subscriptions from Apple are billed - Apple Support Like I said earlier though, even if you have account balance, Apple might want to see another, more open, payment type such as a credit or debit card, even if it ends up taking the money from your account balance.
Refer to this page for Apple Support features ➔ Contact - Official Apple Support
Select from the presented options until you find a solution for your issue, or see if there is a chat or phone call contact method offered lower on the page under “Get more help” (you sometimes have to narrow down the options multiple times before this is shown). If you do not see your issue, keep experimenting with any series of selections until you reach one that offers a chat session or a telephone call and get the representative to redirect you.
This support article has various country telephone numbers for contacting Apple for support and service ➔ Contact Apple Support - Apple Support For some countries look under “Other” listing at the end of the list. Not every country has telephone support, and phone numbers may only work when calling from the same country.