If you want to decode transmissions from common weather sensors, be sure to check out rtl_433 [https://github.com/merbanan/rtl_433]. If you have and RTLSDR dongle, it should just work.

RTL-SDR is an inexpensive way to get started, only a receiver though. Transmitters are more complicated (legally) since a lot of spectrum is off limits without a license in most jurisdictions. They have a kit with a couple basic antennas to get you started.

https://www.rtl-sdr.com/buy-rtl-sdr-dvb-t-dongles/