Knowing what is going on at a time when internet has gone away/shutdown will be critical. News in the USA media is so poor that shortwave offers much to consider. There is alternative media, albeit questionable, and Amateur Radio net discussions, plus Pirate Radio and freecasters. Not going to discuss transceivers in this comment, or scanners, nor satellite sideband listening. There are many Ham Bands above the -0- to 30,000 Herz coverage range of the Shortwave Receiver. No discussion of those here either.
What you can find in the airwaves using a decent quality, selective tuning and contemporary designed Shortwave Reciever include Utility Bands, Commercial Bands, AM broadcast, Amateur Bands, Military Transmissions, Time broadcasts by USA and Canada, and other Government functions and Agency Networks. Many of the same functions from foreign broadcasters and users.
Knowing when to listen is also important. Shortwave propagation depends on skip and solar radiation to excite the signal and bounce it around the earth. We are supposedly entering a Solar Maximum period again, so SWL will be good with many signals heard that otherwise could not be. Basically, the 0-8khz spectrum is an evening proposition. If listening to 120 meter band 1,800 to 1950 hz, you won't get decent reception until after the sun has set. The 40 meter band from 6950 to 7200 is good late afternoon until morning. The higher spectrum bands come in during daylight, and need skip to be very active. The long-band frequencies can be decent most any occasion, but have limitations.
The American Amateur Relay League ARRL has great amounts of information in their huge compendium of publications and especially the ARRL Handbook. Lots of websites done by Hams that explain propagation and how-to make a proper antenna and setup a listening post. Google is your friend, or look at your library and the publications cited below, especially Monitoring Times published by Grove Enterprises.
As to radios, none of the small traveler size World-Band radios are worth much in my experience. I have broken 3 Sony radios over the years, back when I used them often. Touch pads break or the computer chip goes defective. They are just not made for regular SWL service. Once in a while use, maybe they hold up. For sure, if going this route, buy the AC adapter and some kind of earphone or set of headphones.
There are lots of inexpensive/cheap chinese radios sold these days. Back in Y2K era, Grundig and others came out with crank-dynamo gizmo radios often incorporating a flashlight and other functions. Avoid these like the plague. The original BayGen handcrank radio may be an exception, but other emergency radios are just going to disappoint. For the money, no big deal if a $60 unit (or cheaper) craps-out, but do you have a Real Radio and a Real Antenna, plus decent headphones to aid your listening? A digital display Shortwave Receiver is what I'm talking about, or an Amateur Transceiver that covers all bands from 50-30,000 hz. Don't need a ham ticket to own a transceiver.
Aside from listening to the international SW broadcasters, you'll need Upper and Lower Sideband capability. A BFO or beat frequency oscillator was the high-tech means of tuning up/down on a given signal 50yrs ago. Now electronic switching and mode selection do the chore way more effectively. Great fun to tune-in a signal, but slow and demanding. To my mind, you listen to Shortwave for information and you may only get one shot at hearing it. Don't mess around with old gear. There are enough challenges to hearing a weak signal as it is...
Even the big table-top consumer rigs are way more robust than the miniatures. Talking a bout the Sony 2010 and various Grundig Satellit models from 500 to 800 series. Supposedly some guy is selling refurbed Zenith Trans-Ocean radios on ebay. They were cool in their day, but even the Panasonic 2800 from the 70s had a digital readout. Really don't want the old BFO control if your in a survival situation. You may only get one shot at hearing a message/broadcast in the clear. As far as old Hallicrafters and earlier hobbyist gear, forget them. Many are collectible, but not for ease of use or signal processing clarity. Old Collins gear and other legendary receivers would be great for collector or to serve an advanced listener who knew the machine and how to employ it, but for our purposes we want fast signal processing, immediate access to clarity and ease of use.
If you take your communications needs seriously, you get something like a 90s era Drake R8, Icom, Yaesu, or Kenwood general purpose receiver and if it needs an adapter to run from a 12v battery you get it. You also get a real antenna like a tuned dipole with a balun as your connection point and run PL259 terminated balanced feedline. The best deal of all time was the Drake R8 series because of the standard 4 filter widths and other top-notch features like dual antenna inputs and dual vfo, 100 memories in the first models and variety of modes and search/scanning; not to mention, computer interface.
There are plenty of computer interface software which mimic a Shortwave Receiver, yet relying on one of these is foolish. Pretty damn impossible to repair a motherboard or other computer component. Ham type SW sets are more repair friendly. If buying used, I'd recommend buying from a bonafide Ham Dealer that guarantees they've inspected and done a 24hr continuous play test of the gear to ascertain function. Also specify you want any computer interface also tested and would like to acquire software and cabling with your unit.
The large table-top portables that Sony and Grundig, also Motorola and Phillips sold are also very decent; just not as serviceable and robust as the Ham Quality Gen Purpose Receivers. Your gonna need a real set of quality headphones with full-size not a mini plug. The lightweight stuff, even expensive senheiser, sony and other will not take the constant usage. You want full-enclosure and padded ear cups, not the foam junk made for gizmo electronics.
Something else you might want is a tape recorder you can run while listening. A VHS machine can be used to record up to 8hrs on extended mode using 160 tapes. Maybe you have software to record to a RW DVD with a straight line-in function? Even better.
Got a Frequency Guide? Monitoring Times still publishes shortwave broadcaster time logs in every issue. Kinda spendy these days, but worth it if you don't know who and where to listen. Grove Enterprises used to publish a large bound book detailing all the General Coverage frequencies with a large section on Government Agency Networks and military bands. Can probably find various frequency lists on the internet if you search.
To get an idea about pricing, ebay is pretty much a dead horse compared to years ago, but some still sell there. Amazon might be another venue to watch, but ebay will give some idea of prices and show some obscure eqpt/accys. Icom and Yaesu seem to be the strong ham-gear survivors. An FRG 8800 or 7700 is a decent rig, the Icom R-71 and 75 series are better. Kenwood R2000 and 5000 were in-between the Yaesu and Icom in their day. Be sure of parts and continuity if buying Kenwood. I have an R1000 and it has been dependable and robust.