The best stuff is either up on the satellites and/or heavily encrypted up to wazoo- but there's some interesting stuff on HF nonetheless.
If you regularly watch the UDXF, you'll find a lot of folks using SkySweeper or one of the very expensive Wavecom or Hoka 300-32 units. But just to get your feet wet, I would get a copy of PC-ALE. If you've been listening on the GCS system, from time to time you will hear a warbling sound, followed, sometimes, by a station. That's ALE - we have a section in our Wiki that talks a little about it. It's freeware.
It takes a little bit to learn how to read the text that results - you would be primarily interested in knowing who is signalling. Once in a while, operators will insert a text message, and that might tell you some more about who is using the frequency. It's very much a detective game.
I would also get something so you can copy the SitorB weather broadcasts from the USCG, as well as the various FAX stations around the world. There are a couple - such as SeaTTY - which are quite inexpensive.
Just keep in mind that there are lots of modes on HF we will never copy - It's much harder to find something that you can read, and that's part of the game. Our utility monitoring wiki has links for PC-ALE and for Utility Monitoring Central, which has a seperate page dedicated for just software decoders.
73s Mike