There are quite a few inputs into that system. I'm sure an NI person will get on and recommend something. You may want to try selecting components through the website and talk to your local NI salesperson.
To me it sounds like you would need a PXI based system. I would be a Windows based controller and have numerouse PXI slots for data acquisition cards. Considering the high channel count, you may want it to be a hybrid PXI/SCXI. We have one of those. There you have multiple cards in the SCXI part of the chassis to handle signal conditioning for things like the thermocouples and RTD's and will do multiplexing (assuming you don't need to read all of those channels simultaneously). It won't be a cheap system. You may have some sticker shock. But with right kinds and quantities of DAQ cards and SCXI modules, you should be able to build a system that can handle those channel requirements.