I suppose this is now a Windows-only issue.
Problem: iTunes stops at "Verification is required. Please click Billing Information", or similar, but when you click the "Billing information" button, nothing happens. Prevents you from buying anything.
Solution: There is something wrong with your Apple ID that needs to be updated.
The "Billing information" button is supposed to take you to a web page where you can sign in using your Apple ID, where you can view, edit and update your billing information. However, the iTunes button doesn't always work, making it seem like iTunes itself is broken.
Most likely there is some security or billing update that needs to be completed, like 2-step verification or updating your credit card information. Neither of these can be done in iTunes itself; they both need to be done at the Apple ID web site.
So, the solution is to:
• Go to appleid.apple.com and sign in.
• Check / update your security settings and billing information.
• Restart iTunes.
You should be able to purchase things using iTunes as normal.