FabrizioF wrote:
Using the Time Machine backup system, does it backup my whole system (Accounts, AppleID, and so on...)?
Here is what a Time Machine Backup does:
Back up your Mac with Time Machine - Apple Support
"Use Time Machine, the built-in backup feature of your Mac, to automatically back up your personal data, including apps, music, photos, email, and documents. Having a backup allows you to recover files that you later delete or can't access. Learn how to restore your Mac from a backup."
Personally, if I was getting a new computer I would only transfer my data and reinstall any apps I wanted. The reason being, with new hardware maybe old apps will no longer run.