Definitely going to second getting a weather radio that includes a power bank and a light. Alternatively a Baofeng and program in NOAA frequencies (they receive it quite well, and with correct programing you won't accidentally transmit).

That said, if you can spring it, getting a weather radio with digital tuning makes your life a lot easier. Short wave reception on these tends to not be great, but that's like expecting the calculator solar panel on these to charge very much too.