Normally I SWL (Short Wave Listen) on my Yaesu FT 757 GX MK 2 and a 100' low band antenna, but that's overkill for most listeners.
You can easily get by with a Yachtboy 400 by Grundig (gettum off ebay) for around $70 bucks. Add a 100' or so piece of wire as high as you can get it then wrap the wire around the antenna four or five times and you will have a shortwave listening radio that will do you well from AM radio band to 30 mHz for less than $80 bucks.
Of course, better radios are more expensive -- but the Grundig gives you AM for all the AM and shortwave broadcasters as well as USB/LSB for things like hams, military, commercial airliners, CIA "numbers" transmissions. Before I had my ham antenna put up I listened on 1.8 mHZ for the ARRL 160 Meter Contest and could pick out individual CW (morse code) signals very easily. That's when I knew the Grundig was a keeper. Plus it's small size makes it highly portable for trips to the beach, vacation, cruise ships, or even taking it to the big game to listen to the play by play.