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Rather than record at the desired final bit depth (let's say 8 bits for low-bandwidth distribution), with digital recordings one can record at greater bit depth and set the recording level relatively low (say 10 dB to 20 dB below the -0 dB distortion level). This retains plenty of dynamic range but avoids the risk of speakers who are louder than others creating clipping, which will result in unpleasant sound quality.
When recording with a computer, the greater the bit depth you record at, the more time and disc space will be used. See Bit Depth for more explanation.
There are also pros and cons about recording at different sample rates. The sample rate of the recording determines the highest frequencies that can be captured. Generally, lower sample rates are acceptable in speech recording but are not in music, because voices (especially male) have a lower upper range of fundamental frequencies than instruments. Also, by the nature of the different sounds made when speaking and singing, it's less important for quality reasons to capture the higher overtone frequencies in speech. In any case, the higher the sample rate you do record at, the more CPU time and disc space will be used.
Pros and cons
When in doubt, use Audacity's default project settings of 32-bit float sample format and 44100 Hz sample rate for your initial recording. It's always possible to size-compress the file later to take less space, for example by exporting to MP3 (which is lossy), or to FLAC (which is lossless).
32-bit float project format has many advantages, including no reduction of signal-to-noise ratio when applying volume changing effects, and faster processing. Default export is to 16-bit 44100 Hz WAV (or AIFF on Mac computers). That default gives you equivalent to the quality of audio CDs, and is lossless, though not size-compressed.