Re: This "sounds" like a great antidote for nostalgia!
There was a strange phenomena with choosing the cassette player to use on a computer. The thing was that more expensive did not always mean better.
Rule 1. Only use a mono cassette recorder. If you had to use a stereo one, only use one channel, and you may find exchanging tapes with other people difficult.
Rule 2. Get one with a pause button
Rule 3. If using a BBC Micro (or some others that copied it), get one with the microphone start/stop 2.5mm jack
Rule 4. Cue and Review capability was very useful
Rule 5. Get one that allows easy access to adjust the azimuth of the record/playback head
Rule 6. Speed stability and distortion (like clipping), and mains hum will cause you problems, so get one that sounds OK when playing music
Additional factors
Automatic gain control (auto recording level) can be either a good or bad thing. When implemented properly, it can be good. If you can turn AGC off, and adjust the recording level manually, that's even better.
If you can find one that allows you to listen to the signal while playing back, or when recording, that is tremendously helpful.
I bought a reasonable quality Panasonic slim casette recorder back in around 1982. It was around 15 quid, more expensive than most cheap ones, but worth the extra money. It didn't have the 2.5mm jack, so I added one into the power line to the motor. I also drilled a hole to get access to the screw that adjusted the azimuth while playing. I used this very successfully with ZX81, Spectrum and BBC Micro, and it's still knocking around somewhere even now. The WH Smiths Data Recorder was a very safe purchase, having almost everything described above.
I've mentioned azimuth several times. If you couldn't read a tape recorded on someone else's recorder, adjust the azimuth until it sounds as bright as you can, and try again. It normally helped (if you had a tone control as well, turning up to it's highest treble setting could also help). If you changed it, reset it in a similar fashion while listening to a tape recorded on it before you fiddled. If you screw it up, adjust against a commercially created tape. These were normally OK when it came to azimuth.