Sorry, completely disagree with this.
A decent record deck + cartridge can have usable output (with the right record) up to 40 or even 50 KHz. This is appropriately captured by 96KHz sampling rate. It's not really important, but this is *bandwidth*, not dynamic range.
Dynamic range is captured by the bit depth. 24 bits will ensure that everything on the record will be captured. It won't be fully used (nothing in nature has 140dB+ of dynamic range), but it will ensure that everything on the record is captured. 16 bits is not enough, especially because the peak levels on a record can vary dramatically from one record to the next, and PCM audio distorts hugely as soon as you go a tiny bit over the maximum level. Because of this, you need to allow a fairly large amount of headroom, meaning the quiet parts of the signal will be down below the minimum that 16 bits could capture.
BTW, the human ear is fantastically good at extracting usable signal amongst a sea of noise. I've seen it stated that it can listen down into the noise floor by up to 20dB, basically by differentiating between the repetitive noise and the constantly changing music signal. This is the same feat as when you can make out what a colleague is saying despite being in a factory with huge amounts of machine noise.
The quality of the audio equipment and the expertise of the person performing the transcription will massively affect the quality of the resulting digital recordings.
There may also be a temptation to "improve" the signal by removing clicks, rumble, surface noise, etc with digital post-processing. If you want to go down this route I would strongly suggest that you also keep the unprocessed original transcription, as future technology may be able to do a much better job and recover even more detail than can be achieved now.
I hope I've understood your postings to say that you will be retaining / protecting the original media, as these are much more likely to survive over the decades (and even centuries) then your digital copies. At least the vinyl might, if it is stored correctly (and strangely the audiophile community reckon that vinyl needs to be played occasionally to stop surface noise from accumulating).
We have entered an era where we are losing our history. How many people still have the equipment to read MFM hard drives, 5.25" floppies, ZIP discs, QIC, 8mm or Travan tapes? Only museums. As soon as someone looses the will to continually copy their data onto the latest technology, it will rapidly become unreadable and inaccessible.
I know it's hardly authoritative, but I am currently reading an SF novel ("Glasshouse") where one of the major themes is an almost complete ignorance about 100+ years of history starting at the last part of 20th century. Before then, stuff was printed on paper which survived and was not obscured by DRM. After the end of this period, society had learned to retain and archive its digital history.