FLAC is the most common format, it is non-proprietary, it is lossless, but compressed (as in ZIP). Best for storage.
If you need to process the recording you are going to use an uncompressed format to lighten the load on the CPU, such as WAV and AIFF (or most serious software will do that for you in the background).
Most music is distributed at 44.1khz 16bit - even if now some providers offer 24 bit - and some offer lossless like Tidal (which uses FLAC in the background).
Home studio production is usually done at 44.100 or 48.000khz 24 bit, semi pro at 96khz and pro at 192khz (not always).
The higher up you go the better your equipment must be - and the marginal improvement can be very very slim or noticeable at all as you move up.
So most likely depending on the source you need to record 44.1khz 16 bit is good enough for archiving (eg. CDs). Obviously there is not much of a point archiving mp3 material other than in it’s format - the case may be different for some more obscure codecs which may be harder to find support for in the future.