Was briefly looking at these amazing 32-input fully differential input cards from General Standards, until the moment that it dawned on me that I don't need all 32 channels.
Here are is the 32-channel 16-bit ADC family from General Standards. I was surprised that their input noise is unexpectedly high considering that the similar analog output cards have low noise options. http://www.generalstandards.com/view-products2.php?BD_family=16ai32ssc
This shows that the input noise is 0.5 mVRMS; typical, all ranges; 0.01-50kHz. http://www.generalstandards.com/specs/66_16ai32ssc_spec_110614.pdf
Here's all of General Standards' analog input boards, a pretty amazing selection: http://www.generalstandards.com/analogio5.php
Basic google searches led straight back to National Instruments analog input cards
Here are the basic analog input modules, with the simplest being the 8-input PXI-4300: http://www.ni.com/en-us/shop/select/pxi-analog-input-module
The datasheet for this card doesn't just come out and tell you the input noise, there's a whole set of formulas which add up gain error, offset error, and noise based on input range, resulting in essentially a set of noise curves although they don't present it as such. The 6221 has the following expected noise and accuracy: 1V scale: 38 uVrms noise, 323 uV accuracy, 10V scale 171 uVrms noise, 2495 uV accuracy. http://www.ni.com/pdf/manuals/375476c.pdf
The NI "M Series" seems to be higher accuracy (lower noise) http://sine.ni.com/nips/cds/view/p/lang/en/nid/201759
This datasheet for the M series 6280 follows the same procedure for adding gain error, offset error, and noise together to show much better accuracy readings. In summary, this card has the following expected noise and accuracy: 1V scale: 7 uVrms noise, 70 uV accuracy, 10V scale 60 uVrms noise, 980 uV accuracy. http://www.ni.com/pdf/manuals/375217c.pdf
Here is a PXI-6221 National Instruments 16-bit 250Ksamples/sec Analog IO card that seems to be from their "Legacy" series: http://sine.ni.com/nips/cds/view/p/lang/en/nid/14133