Hi, if you are able to program in C#, and have a GPIB card, that's the best way to do it.
Any other programs like BenchView either are limited in possibilities, when it comes to processing data life, or using several instruments, or these programs cost a fortune... Same goes for BenchView, if you want unlimited time logging.
I'm doing all my long time data logging in Turbo Pascal, so I have maximum access to hardware.
I got a GPIB adapter from National Instruments, which comes with appropriate SW interface for all languages.
(I'm too lazy to switch my library to C)
You may get the old HP3488 switching system on low budget , base unit and a few switching cards for under 100 bucks, it's also GPIB based, anyhow.
You did not tell, which DUT you want to measure for noise / stability.
There's the DMM project of TiN, for determining the noise figures of different meters, including the 3458A..
There you can see, what is the DMMs intrinsic noise, depending on NPLC..
So you can chose NPLC for needed zero input noise; 3458A currently is one of the best meters you can get for that purpose.
If you have a DC voltage source as DUT, you might get some ideas about the order of noise levels in the Ultra LTZ1000 reference thread.
Somewhere from page 16 onwards, I published my noise and stability figures for this reference acquired with my 3458A (order of 0.1ppm of 10V ~ 1..2 µV noise).
For (long-term) stability measurements, it's mandatory to have absolutely stable room temperature during measurement.
It's <= 0.2°C in my basement.
Frank