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 only be 0.011% at the point where the sine-wave has the greatest slope. And 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 things like military submarines which must perform dead-reckoning requires bandwidths in excess of 1kHz. This 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.