Is there a preferred order in which to apply (analog) filters in a chain?
There is no 'one size fits all' solution.

It depends on the detail of your individual amplifiers, and your input signal.

First, you have to see whether it's even theoretically possible to build a signal processing chain from your chosen amplifiers, for your chosen specification. Your specification should allow you to derive a dynamic range for the system. This is the difference between the minimum signal (usually defined by noise and signal offsets) and the maximum signal (usually defined by some measure of distortion (harmonic, intermodulation, spectral growth) slew rate, or even clipping against the rails). Each of your amplifiers will have a dynamic range. All amplifier dynamic ranges should be greater than your specification dynamic range, the greater the margin the better. The amplifier with the smallest margin is the one to worry about first. If your signal, or your specification has a small dynamic range, then your job is easy.

The amplifier dynamic ranges will apply at an optimum signal level. As you move lower than this level, the effect of noise will increase, higher and you get more distortion, both decreasing the dynamic range. This defines a signal level profile through the signal processing chain.

Does your input signal have any defects? Much HF noise? Put a LPF first, to protect the slew rate of later stages. Much DC offset? Put a HPF first, or a differential stage, to remove the DC and centre-up the signal for subsequent stages. 

Finally, arrange your stages in an order that meets the signal level profile. If there are lots of ways to do this, lucky you, your job is easy. If there is only one way (let's say it's an off-air signal, so you need a bandpass filter and LNA first) with subsequent stages of gain with increasing signal level handling, then it's straightforward. If there are no ways, then find the limiting element, the one with the lowest dynamic range, build or buy a better one, rinse and repeat.