1. Use a simultaneous sampling ADC. Difficult hardware but easy software. Can get away with the lowest sampling rate.
 
 2. Just sequentially sample through the channels with a multiplexed
    ADC.
        You can sample so much faster than a mechanical system's response
        that the error probably doesn't matter. Then just treat all samples
        taken in the same channel scanning cycle as simultaneous. Simplest hardware and software but needs the
        fastest sampling rate.
        
    For example, suppose we have 16-channels and a sampling rate of 1MSPS to spread across those channels. Let's assume our bandwidth of
    interest is 1kHz. To that end, let's pretend we are inputting the
    same 1kHz sine-wave (the highest frequency component in our
    bandwidth of interest) into all the channels. Between the two
    channels spaced farthest apart in the same scan cycle, the
    difference in the reading would differ by no more than 0.011% of full-scale (i.e. at the point where
    the sine-wave has the greatest slope). 0.011% of full scale exceeds 13-bit resolution.

    I was also being conservative choosing 1kHz. Although your mechanical
    bandwidth may exceed 1kHz, your sensors are probably just
    commercially available MEMs sensors for the smartphone or automotive
    industry and therefore do not exceed 300Hz.
    
    I seem to recall reading that it has been found from experience that
    military submarines require inertial measurements to employ gyroscopes and/or accelerometers with bandwidths in excess of 1kHz to acceptabley perform dead reckoning. That is a big huge submarine
    however, so the bandwidth to do the same on much smaller platform
    like what you are working on is probably higher. However, it's moot
    because the submarines requires very high grade optical gyroscopes
    to do this which your sensors certainly are not.
 3. Sample channels sequentially like #2 and use zero stuffing and decimation to digitally interpolate data points as if you did simultaneously sample in hardware. Detailed process is here:  https://www.ednasia.com/sample-multiple-channels-simultaneously-with-a-single-adc/ Simplest hardware but most complicated software. Can get away with a sampling rate between the other two methods.

Architecture is not important but if you need high speed sequential sampling or use an ADC integrated in an MCU (both of which will go hand in-hand if you are trying to simplify your hardware), you will probably end up with a SARs ADC. Don't forget your anti-aliasing filters.