I don't think there is one universal approach to tool selection, let alone to tool selection for test automation.
There are many areas and questions you need to consider before going for a particulat tool or set of tools:
- How mature is the test tool? Is it available in a stable version, or is it still under heavy development?
- How well can you use it? How well other testers can use it? If it's a great tool but nobody has an experience with it, it's probably not the best option since you and your team would spend additional time and money on learning the tool.
- How big a community is there around the tool? The more people use the tool, the more support you can get when something doesn't work the way you expect. Some obscure tools will probably not be maintained much, so if there are some bugs, and there almost certainly are some, it'll be hard to get them repaired.
- How much does it cost? Not all the tools are for free, do you have a budget for it?
- How well can the tool work with your product? Some products might be specific and they need specific tools, sometimes even created in-house. Can you try out the tool first and decide later?
- What is the future plan for the tool? Is it still widely used or do you see than other tools have been replacing it? You don't want to end up with something that nobody uses in half a year.
There're more and more questions, but if there's something you might take from my post, it's the fact that you should try out the tool. Give yourself some time to actually use the tool on a real project, ask other testers to use it as well. Then talk about how valuable the tool is to you and your project. Then you should have enough information for making a good decision.