I developed a system very similar to what you described a few years back. I believe we used 5B modules for the signal conditioning. SCXI is one of my favorites, but it can get a little expensive. There are other options available also.
It might be useful for you to have a contract programmer write your code for you. You will learn a lot from the code, and your system will work much better than if you try to put it together from scratch without any experience. The NI classes help some, but there is no substitute for years of experience.
I am not familiar with the Vishay equipment, so I can't help you there.
Bruce
Bruce Ammons
Ammons Engineering