Help on Selecting a digital multimeter (DMM)

Hello, I'm a graduate student who is preparing to purchase 1 or 2 DMM's for my research project. I know little about electronics as I am in mechanical engineering and would like to see if anyone has some advice to offer with regards to the DMM's I am considering.

I plan to measure the direct current potential drop of a metal sample that I have in fatigue testing. I have performed tests using another lab's equipment. Using a power supply, I intend to provide a constant direct current that will vary between my tests in the range of .5 to 10 Amps. I will measure the potential drop in two locations of my sample. The potential drop is expected to range between .1 and 50 millivolts. I would like a resolution of between .1 and 100 nanovolts (cost is an issue). Measurement speed is not a huge issue, and at most I would need 10 measurements per second. However, the duration of my tests will last on the order of weeks.

To the best of my knowledge, I will need 1 power supply and 2 DMM's for this project. Currently I am considering 3 different DMM models and would like to know if anyone has a bias for or against a particular model.

These are:

Picotest 3510a-100 nV resolution
Keithly 2182a-1nV resolution
Agilent 34420A-.1 nV resolution

Suggestions as to what power supply to use would be welcome as well. Thank you for your help.