The main thing to consider when choosing a WiFi extender is whether it supports the WiFi standard offered by your router: this will usually be written somewhere on the actual device and be something like 802.11a or 802.11b. You don't need to know what this means, only that it's supported.
If you have only recently bought your router, though, it's probably got a faster standard than most, and you'll want a WiFi extender that can take advantage. The slightly confusing thing here is that the latest standards – 802.11ac and 802.11ax – are also known as WiFi 5 and WiFi 6 respectively. But as long as you understand they're the same thing, you'll be fine. (Note that WiFi 7 isn't expected to arrive until 2024).
Beyond that, the main way to choose your WiFi extender will come down to price, the amount of area it covers (usually measured in square feet or square meters), and the speeds it offers. Plus, if you want to plug in wired devices to your WiFi extender, you'll need to know what ports it has.