Payment method

You should be able to set it up without a payment method:

Create or use your Apple ID without a payment method - https://support.apple.com/HT204034 - "When you use your Apple ID to sign in to the iTunes Store, App Store, or iBooks Store for the first time, you're asked to enter a payment method so that you can purchase items from the store. Follow these steps if you don't want to associate a payment method with your account."

Unless an app is free you will, of course, need a payment method. There's various ways to pay for items in the iTunes and App Stores.

- Add money to your Apple ID balance - "With the payment method that you have on file, you can add funds to the Apple ID that you use for iTunes & App Store and iCloud Storage purchases."

https://support.apple.com/HT208687

- Payment methods that you can use with your Apple ID - https://support.apple.com/HT202631

then

Change or remove your Apple ID payment information - https://support.apple.com/HT201266

- Create and add money to an iTunes Pass - "At Apple Stores and select retailers, you can add store credit directly to the Apple ID that you use for App Store, iTunes Store, and iBooks Store purchases." - https://support.apple.com/HT203021

- Redeem App Store & iTunes Gift Cards, Apple Music Gift Cards, and content codes - https://support.apple.com/HT201209

There's no list but from posts here it seems there are some things that absolutely require a potential payment method such as a credit card number be entered in order to use a service.