Amplifying and Measuring Bipolar Signal
Is using an instrument amplifier the best way to go about this?


Yes it is unless you are going to use an isolated combined ADC and InAmp (as purveyed by Analog Devices and very nice they are too). I'll try and remember the part number if pressed.

Given that a thermocouple will likely be deliberately or inadvertently shorted to ground/earth I have to suggest using an InAmp with a split rail supply because the polarity may not be known and the signal voltage may indeed go negative to ground. Also it keeps open options for best common mode noise rejection. You can make a negative supply from a positive one - there are chips that do this and quite low power ones too.

Then, what you do is offset the reference pin on the InAmp (pin 5) to the middle on your ADC range so that you can take a full measurement if polarity is switched. Top half of the ADC range deals with correctly connected thermocouples and the bottom half deals with incorrectly connected thermocouples.

Given also that the input offset of your InAmp is roundabout equivalent to 1 degC you may choose to multiplex (using a DG409 for instance) so you can auto zero. This then gives you the possibility of also measuring a cold junction reference and maybe a precision voltage reference to give you some accurate gain calibration point.

To what extent you go down this line is up to you.