Ask HN: Looking to purchase a software-defined radio, any advice?

I'd like to use it to experiment with and explore interesting parts of the spectrum. For example: decoding digital television signals, seeing what my cellphone sends/receives and how it encodes it, downloading weather satellite images, and so on.

I've no experience whatsoever in radio, only in software. Where should I start? What should I buy to begin with? Any general technical advice?