Problem getting Apple TV, needs iTune account but...

it tells me I have to get an iTunes account first.

Your Apple Account needs to be activated for iTunes Store services.

This account needs all the information as asked for, including your name, DoB, country (state), a verified email address (when creating the account, respond to test message!), and a valid payment method (as issued in the matching country). The linked payment method should be pre-authorized for any future charges, when that applies, like for subscription fees.

It is highly recommended to add a trusted phone number for two-factor authentication to send verification codes to.

Then it wanted the payment details. I always use Paypal, so it sent me to the Paypal log-in page, but for the password, Apple had automatically entered my Apple account email address, invisibly. And that will not work because I keep one separate email address for Paypal only.

Why is it so very complicated to get Apple TV? Is there an easier way?

Try being signed in to the PayPal site, before the Apple TV app wants to go there. That should then skip the sign-in page, I think.

They want the payment info even though there is a free trial.

That is part of the deal. They want the payment method, so that ① an auto-renewal after the trial can be billed (if you don’t cancel before the end of the trial), ② users may choose to get additional digital goods and services, ③ so that users can be limited to one trial per person, and ④ parental controls on the web can be authorized.

I might try to remove all accounts - the Apple TV one and iTunes, and start again from scratch.

Those should be the same. One Apple Account for Apple TV+ and iTunes services.

It seems like Apple is asking for payment details because your Apple ID is linked to iTunes, even if you're not trying to buy anything. To fix this, go to your Apple ID settings and check that your PayPal account is linked with the correct email address. If you're only using the Apple TV free trial, you should be able to skip the payment details by selecting "None." If the issue persists, try signing out of your Apple ID on both your TV and iTunes, then sign back in.

you don't need to download an app you need to make an

apple account (used to be called appleID)

How to create a new Apple Account - Apple Support