Approaching Thermocouples

I want to convert the electrical output of a thermocouple to a unitized digital temperature value stored in an Arduino's memory.

Thermocouples:

1. Produce small signals (~41 microvolts per C  delta temperature)
2. Do not produce an absolute temperature but instead a voltage (current?)  between junctions of dissimilar metals
3. The produced voltage is not linearly related to the delta temperature.
4. The currents produced are very small so the measurement system must have high impedance since  we  will be measuring voltage (not current) we don't want to load it down. We want to look a the potential developed across a break in the current loop, physically located at the cold junction.

Common approaches:

1. Use an digital "all in one" single chip solution that deals with  all of the  physical characteristics of a thermocouple and produces a digital output signal.
2. Use an analog "all in one" single chip solution that produces a high level low impedance analog output. 
3. Use a precision instrumentation amplifier with high input impedance, and low offset voltage , An AtoD converter with an abundance of bits (so we don't need so much gain in the InAmp and handle cold junction compensation linearization and unit conversion with  semiconductor temperature sensor  and software running on a microcontroller. 
4. Use the crappiest analog components possible, the least precise,cheapest AtoD converter possible, use the worst, cheapest cold junction sensor  possible. Layout the board for thermal stability and low noise and leakage, design in good thermal contact between the crappy temperature reference and the cold junction. Choose terminal blocks (metallic composition?), trace widths and thicknesses for thermocouple measurement. Add a terminal block "cozy" to enclose the cold junction terminal and temperature reference to get the cold junction terminal temperature closer to the cold junction sensor measurement.  And still produce  a temperature measurement with the  required accuracy and precision and low cost.

Approaches 1 and 2 are constrained to just a single type of thermocouple, since they are hardwired for a particular type.

Approaches 3 and 4 depend on software to convert raw digital measurements to temperature units for any type of thermocouple.

Any of the approaches can have an analog multiplexer added to measure more thermocouples (sequentially)  reducing  measurement rate and the cost per measurement.

We would like to be able to detect faults in the measurement, such as opens and shorts. (some of the all in one solutions have this feature built in)

Questions:

1. Approaches 1 and 2 are uninteresting (except for the PCB thermal design aspects) so they have no questions
2. How to get low offset voltage and high input impedance with approach 3
3. How to get low offset voltage and high input impedance with approach 4
4. How to model the system to determine how good each block must be in approach 3?
5. How to model the system to determine how crappy each block can be in approach 4?
6. How to test that the measurement system meets the design goal once it's built?