I've been trying to subscribe to Apple TV on my ROKU TV. I have an Apple account.
Verify that you made your account complete: user details, email address (confirm the test message), and payment method.
How to create a new Apple ID - Apple Support
Manage your Apple ID - Apple
Payment methods for subscriptions should support automatic and periodical charges.
The app says I need an ITunes account. Do I really need this?
Your Apple ID account needs to be ready for use with the iTunes Store. As above. That is needed.
More$$$.
No, subscribing to Apple TV+ is the only fee, if you stick to Apple TV+ content. Other content in the Apple TV app is not included in this subscription, and may require additional payments, as indicated in the app.