Its more about the tests your trying to perform as apposed to a "check list". Because there are many metrics for different things, refresh rate means very little to a software application but means something to a monitor. So the check lists are modified dependant on what you're trying to test, and how the test is being run. For example here are some common tests...
If your trying to see the ability of the hardware you're doing "performance metrics", there are software applications and external devices that do those for hardware. Such as a video card measuring frames per second on a sample piece of video.
If you are trying to see physical limits of a piece of hardware it is sometimes called "stress testing" These are usually done in controlled environments. Such as raising voltage on a piece of memory to see when it starts to perform unreliably.
For applications you want to see how easy it is to navigate there are "usability tests". And there's a whole subset of test that are done to ensure QA has done its job. But these usually occur before you get the product.
When you are talking about pricey items. You can do what's called a "Proof of Concept". To see if the application or hardware meets your requirements before you buy it.
Such as a backup application. the POC would detail how you want hourly backups of your data set. And you want it to be able to restore data at a rate of 30minutes per 1TB.
But you ultimately just need to ask a simple question. "What do I need it to do?" (You may have multiple answers or more questions from there)
Because vendors publish stats/feature information for a reason, 1. To show you how awesome the product is and 2. As a means of comparison. Vendors use "ideal" conditions to make their product look as good as possible. And in some cases the vendors have third parties do the testing for them to ensure valid results. Thus making them fairly comparable.
So if you have particular item(s) you want to recommend, ask about them, and describe what aspect you want to test.