@LarryC did a fantastic job of rebuilding the AC system back to pretty much stock configuration. And an even better job documenting everything. Kudos to him for his excellent work.
The only thing I'd suggest different is considering
not using any of the original fittings/hardlines and sensors/switches. For one thing there is a much simpler (and more efficient) method that eliminates all of the sensors and switches that Fiat used. It is a "trinary" switch that mounts directly to the receiver/dryer ("filter"). This will require a little rewiring (which mine needed anyway, and is much simpler than original), and different fittings (which I suggest replacing regardless). But given you will need new hoses anyway, with new fittings it is easier to do away with the hardlines completely and run barrier hose for the whole system. That will help to ensure getting the proper fittings to match as well. Surprisingly I also found this to be less expensive overall.
"Universal" components are available for a lot less money than trying to source stock or stock-like replacements. That includes the compressor, condenser, receiver/dryer, expansion valve, hoses, fittings, and trinary switch. If your X came with factory AC then keep the compressor mounts (on the engine) and use a standard/generic "Sanden 508 compressor". It is a direct fit for the mounts, but uses standard fittings, and it is very affordable/easy to source. The factory evaporator is already fitted into the heater box and that box is set up for all of the air controls, etc.. So keep it, but 1) properly flush the evaporator core, 2) replace the expansion valve, and 3) rebuild the heater box as the linked thread recommends.
Therefore you will end up with a 100% brand new system - with the exception of a rebuilt evaporator core.