I can get armchair copy from my now ancient Soft66LC4 SDR, which is I/Q sampled via a sound card, but the attached antenna and the arriving signals are the more the important factors there IMO. It is not much for weak signal work, but it is perfectly fine for listening to lots of powerful shortwave broadcasters.
Alpard, also take note that sampling like up to 32MHz of spectrum can be great, but sampling bandwidth is not an outright indicator of performance.

For example, the mentioned Airspy HF+ models use a 16-bit ADC followed by a DDC for decimation to an 18-bit output, but bandwidth is limited to a max 912KHz. For many people who are casual hobbyists, like me, that is more than enough to *visually* monitor on a waterfall at a time.
Sure if you are recording and/or streaming from multiple bands, like Chris does, then admittedly large sampling bandwidth can make more sense.
There are a litany of other specs involved, too. Internal noise floor, sensitivity, selectivity, dynamic range, etc. From your other thread regarding receiver overload, it seems like selectivity might be a distinct concern for your particular situation.