Let me summarize a few things said here and reiterate a few other points:
For the best possible long-term archival, LP -> lossless is the only way to go. You could then compress your lossless tracks to a lossy format for playback on your current players.
Lossless codecs (from most common to least common) are FLAC, ALAC, and APE. They produce the same result: a compressed, lossless copy of the original audio without any audible changes at all. WAV or PCM files will produce exactly the same audio, but with much larger files, due to the lack of any compression.
For Lossy codecs/formats: MP3 and AAC were mentioned, but I'd add one more, a newer one: OPUS.
You could achieve near-transparent results using mp3, but it generally requires a high bitrate - 320kbps and a good-quality encoder, like LAME (lame -b 320 -q 0 -ms input.wav output.mp3)
The important point is smaller the bitrate, the smaller the output file is. Also, in most cases 24 bit recording are wasted space, even for our audience of audioholics. 24-bit is worthwhile for recording master records, not for end-user playback.
That said, exactly the same audio quality can be achieved with AAC at 256 kbps or 192 kbps using OPUS.
320kbps AAC is 99.9999% the same as FLAC, or at 256kbps with OPUS.
So AAC is more efficient than mp3, but OPUS is more efficient than AAC.
Opus ≳ AAC > MP3
| Bitrate | MP3 | AAC | Opus |
|---|
| 64 kbps | Poor–fair | Fair–good | Good–very good |
| 96 kbps | Fair–good | Good | Very good |
| 128 kbps | Good | Very good | Very good–excellent |
| 160 kbps | Very good | Excellent | Excellent |
| 192 kbps | Very good–excellent | Excellent | Usually transparent |
| 256 kbps | Excellent | Usually transparent | Transparent |
| 320 kbps | Usually transparent | Transparent | Overkill for most uses |