Effect of increasing Detector Range in Power Usage
The sampling rate needs to be at least 2x the highest frequency, in theory.  the lowest frequency has no bearing on the minimum required sample rate.

In any real system, you're going to need to sample more than 2x the highest frequency.  You care about data up to 180 Hz, so the system needs to pass that reasonably unmolested.

You also have to deal with higher frequencies, even if you don't care about them.  If you sample at 360 Hz, then anything higher than 180 Hz in the signal will alias and look like valid signal.

You probably want some analog low pass filtering that rolls off a bit above 180 Hz, so as to not affect 180 Hz much.  This filter needs some room to attenuate the noise to the don't-care level.  Let's say you put two poles of R-C filtering at 360 Hz.  Two octaves above that, at 1.44 kHz, noise will be attenuated by about 15.  Only you can say if that's good enough.

If it is good enough, then you need to sample at least 2x that, or 2.9 kHz.  Now you can apply a tighter filter digitally that, let's say, goes from pass to stop within one octave.  That octave would be from 180-360 Hz, so using this filter you can decimate the 2.9 kHz stream down to 720 Hz.  This is doable with a low end DSP.

Talking about resolution as a function of frequency makes no sense, unless you are trying to measure frequency content, but you haven't said that.  The resolution you get is a function of the number of good bits of your A/D.  For example, 10 bits gives you about 1 part in 1000 resolution.