This is my small project that you can use/edit for your Firefox's home page. I recommend use this home page with New tab override extension and with custom http server.
Picture of home page:
You can edit main.js:84 on whatever search engine you want.
There is two cities already configured by default. If you want to change it, then I recommend you to use open-meteo.com (free service).
You can use default buttons as a template. I suggest you to 128px images for button's icon (if not you can just delete that and keep button with text).
There is MOTD (message of the day) right up from search bar. You can change array of MOTD's at main.js:48