I have a 24-bit ADC sampling at 31250 samples per second. I am collecting these on a wireless device, and sending them in real-time to a PC for recording (and later analysis). My band of interest is 0-1000 Hz and the ADC produces noise which is more or less Gaussian with a level of around 19 LSB RMS.

My radio link has limited throughput, so I cannot send every sample from the ADC to the PC (would require 750kbps) and must instead send a subset of the data (less than about 190kbps).

The goal is to get the lowest possible noise level on a spectrum plot (e.g. using Welch's method) for a given duration of data (e.g. 10 minutes).

With that goal in mind, is it better to average more 24-bit samples together and send the full bit content (lower sampling rate, higher # of bits) or is it better to average fewer 24-bit samples and discard the lower noisy bits (higher sampling rate, lower # of bits)?

If I can discard noisy bits then how many must I keep for adequate oversampling on the PC side?

Is there an alternate processing method which would provide better results than simple averaging? It seems like Delta-Sigma can only be applied while the analog signal is being digitized, not after the fact (and I cannot change my hardware).