It could be worth joining a local amateur radio group, even if you've not done the exams. The charge is a small nominal sum per year, and they might even have a receiver to sell (at least then they can test it for you). Some eBay amateur radio stuff might be over-priced or faulty, and it's sometimes not easy to diagnose a fault quickly enough for a refund (for instance, some faults may only occur in one frequency band or mode, and one might think it's operator error and not device error.
For short-wave (well, HF), it's hard to get a decent handheld (most handhelds are way better at VHF/UHF and above; there are handheld receivers that will tune down to say 100 kHz, but they are only usable at a pinch at those frequencies), but there will be many desktop units that operate from 12V. I think that video is mainly intended for those who plan on using VHF (which is fine of course, but just doesn't work for those interested in HF).
AOR and Yaesu are two example manufacturers. I have three AOR receivers, one handheld and two desktop. The desktop ones are better but the ones I have are no longer manufactured. If I were buying a new standalone receiver, it would have SDR architecture, but I don't have a suggestion since I'd want to be sure before I could confidently state a recommendation!
I think it could be interesting to join an amateur radio club, and see what they suggest or can offer. Incidentally, it doesn't even have to be a local amateur radio club. I'm a member of a club which is 150 miles away from me.