High resolution ADC vs amplifiers
32-bit ADC is misleading. Even at it's highest gain, the noise peak is roughly 60nV. A 5V 24bit ADC is 5/2^24 or 29nV per a bit. So the bottom 9 bits of the 32 bit ADC will be noisy. There are less noisy delta sigma ADC's on the market.




  Would I be better suited to using amplifiers for each individual
  channel rather than using this unit of an ADC? ie using thermocouple
  amplifiers and bridge amplifiers where appropriate?


Depends on what your objective is, if it's lowest noise, an ADC with a mux will always be noisier than a standalone ADC, because the transistors from the MUX are noise sources. 

As far as your amplifier question, again it depends on what the requirements for the project is. But there will be better control over how much noise is in your circuit if you use analog amplifiers, it will also cost more. The ADC also has many digital filters, so instead of using analog sensors and calculating the bandwidth you can change it with software.