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.
LimeSDR are a bit more involved, but like most SDR transceivers still need band-pass filters and power amplifiers to perform well. Works well when combined with a GPS locked 10MHz GPSDO like a BG7TBL. =3
