I too want a dedicated display and decided to use a Fire HD 8 Plus (wo Adds). I actually have a good mount point on a wall with a hole behind it for wired access. I though worst case I would use Weather Underground and their SILK browser. What I found was that I can’t disable the screen time out. I now keep WU and the Tempestwx.com open in Silk browser. But the biggest help is actually Alexa. I can say “Alexa open Silk Browser” and she will wake and open silk with the two tabs. But I can also say “Alexa Smart Weather” and she opens the “Smart Weather” app. In smart weather everything is good except rain fall accumulation is not shown. I report this to support… and I got “I believe it is on our teams roadmap to incorporate our Smart Weather skill with the Alexa Show devices, currently it is only compatible with a voice response from Alexa”. Well Alexa Smart Weather is available, on Fire HD, but I don’t have precipitation accumulation in “Alexa Smart Weather”.
I also want accumulated precipitation on weatherwx.com