What are your criteria in choosing an automation tool?

I have the impression that in many companies when they have to choose an automation tool they don’t really have specific criteria, just pick UFT or Selenium by default because they are the most famous tools.
But since we are good QA (isn’t it) I think that it’s important to have a proper evaluation grid when choosing a tool.
Let’s suppose that next monday you start a job in a new company starting automation testing from zero, what would you do ?
In my opinion, the main points would be:
• Analyze the software to be tested (what kind of tests should you automate? batch ? visual ? just functional ?)
• What are your programming skills and what is the language used by the developers (for example if it’s JS you could look at Cypress/Webdriver.io)
• Budget available
• Security requirements (for example if you can run tests on the cloud)
• Compatibility with the CI/CD tool of your company
• Always do a POC
Other ideas?

I think your main points cover quite a lot already.
• With nr 2 I would like to add: ease of use & if it requires some training/coaching from team members.
• Reporting is also a strong point.
• If there is a lot of documentation of the tool & support for it, you don’t want to pick something like Protractor which is getting deprecated
• Perhaps integration with other tools, not just CI/CD
• Is it scale able? Let’s say you get started with it and other teams seem to notice you
• Mentality of the team