A good vinyl record on a good playing system will have a signal to noise ratio of maybe 60-70dB. A 16 bit converter has a theoretical S/N ratio of 96dB and modern ones closely approach that in practice. So your quantization noise is already 20 dB below the noise off the record player/preamp combination, if not tape noise from the original studio recording.

Going from 16 to 24 bits won't "keep as much information as possible", it'll just waste bits on encoding the background noise more accurately. And a 24 bit converter in a computer sound card is probably using the bottom 4 bits to encode its own noise...
This is what I meant when I said the record player is already the weakest link, echoing M.Ted's sentiments.

24 bits are useful when recording in the studio mainly for the convenience of extra headroom so you don't clip when something comes through louder than you expected when originally setting levels, and 24 or more bits are genuinely useful when doing mixing and complex digital processing, but for a straighforward digitization like this you don't need more.

However it might be worth using a higher sampling rate for the reasons I stated to do with click removal software.

Anahata