No. There are lots of factors involved in recording “best” quality.
Even 8 bit can sound quite decent apart from the sssss that is impossible to get rid of. All digital recording has ssss that is caused by the digital format. At 16 bit the ssss is so quiet that it should be inaudible against the music. More than 16 bit and the ssss is more inaudible In other words, 16 bit is enough for listening in really good quality. For recording you need to use 16 bit or higher, depending on what sounds best.
When recording, 24 bit has some advantages, and when processing the audio, 32 bit float has advantages.
The default format for Audacity is 32 bit (float), and all internal processing is done in 32 bit (float). Working in 32 bit float is highly recommended (and the default setting) because it makes calculation “rounding” errors insignificant.
When exporting the finished, edited and processed recording, 16 bit is enough for extremely good sound quality (and is the bit depth for CDs).
As general “rules”:
When recording, use whatever sounds best.
When processing, use 32 bit float.
When exporting the final product, use 16 bit.
The default settings in Audacity have been carefully thought out and work well. The only thing that you may want to change is if you need the final export in MP3 format, you will probably want to increase the bit-rate (preset “Standard” or “Extreme” work well for music).