Global and Individual Gain Setting on 16 Channel System - Analog Solution
So rule of thumb: if there's no reason to do it in analog (i.e. if your ADC has plenty resolution for you even if you keep gain low), then don't do it in analog, do it digital: A multiplication by a factor in digital domain is deterministic and costs next to nothing. An amplifier being adjusted to a specific gain, that is matched to that of an amplifier next to it: that's a hard task, it involves temperature and supply dependencies, is noisy and expensive.

So, enjoy the fact that you can program this; it'd be stupid to do it in analog if it can be avoided.

For the overall system gain, that makes sense, no matter what.

For the individual channels, you might want to make your gains adjustable just to be able to use the dynamic range of your ADC.

In that case, there's programmable gain amplifiers (PGAs) made in decades or powers of two. Easy, digital, pre-calibrated solution to an analog problem.

If your signal is RF, feasible PGAs might not exist. Then, use a fixed-gain amplifier in every of your 16 branches, and an adjustable attenuator.