Your M1 Mac mini has an on-board HDMI 2.0 port. It would probably be easiest to just use an HDMI cable to connect it to your display. Be sure to use a “Premium High Speed” HDMI cable if you want to use resolutions higher than 1080p.
Alternatively, you should be able to use a passive USB-C DisplayPort cable. But that will consume one of your two Thunderbolt ports, which you may not want to do. I don’t know why people on Amazon say it doesn’t work - maybe they are using computers where their USB port isn’t connected to a GPU.
If you want to drive a display from one of the Thunderbolt ports and also use it for data, then you will need to get a dock, which might cost more than you want to spend.
What kind of dock? You may or may not be able to support an HDMI display downstream of the dock, depending on what kind of dock you have.