1. Use a simultaneous sampling ADC. Difficult hardware but easy software. Can get away with the lowest sampling rate.
 2. Just sequentially sample through channels with a multiplexed ADC. You can sample so much faster than a mechanical system's response that the error probably doesn't matter (i.e. sequentially poll between channels at 1MHz but your mechanical system only has a bandwidth of 1kHz.). Then just treat all samples taken in the same sample cycle as simultaneous. Simplest hardware and software but needs the fastest sampling rate.
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.