Sample rate (samples/second), channel impedance (ohms), signal bandwidth (Hertz) would be good starting points.
Your channel impedance and the voltage range give you the power in your channel. Signal to noise ratios (SNR) is defined in units of power. You can use Johnson Noise to figure out your absolute lowest noise floor, before systematic effects start popping up (like Schott noise, flicker noise, and 1/f noise).
The ratio between your sample rate and your signal bandwidth lets you start to figure out how complex of a filter you need. A first order filter has a slope of 20dB/decade. 5 counts out of 2^32 is -179 dB, so that is nine decades (1,000,000,000:1) or a very high order filter (2nd order filters are 40dB/dec, third order are 60dB/dec...).
Is you SNR and SFDR specification for your A/D greater than 179 dB? If not you will need digital filtering (averaging) to approach that floor. For example, I have a 16-bit A/D (96dB) with a SNR of 80dB, so I don't even see -96 dB until after averaging 40 samples.
Welcome to channel design.
Z