The older GPIB based units pretty much standardized by LabView
There will usually be LabVIEW drivers. Because the communication is ASCII and well documented, it is also easy to develop your own software to interface with them. But as for off the shelf software, that is more limited.
Sigrok has some support, but their support for bench meters is quite limited, and a front-end for DMMs is still incomplete.
I did use a HP34401A a few years back, I had to install the LXI drivers - real pain in the arse.
LXI drivers? Since when does the 34401A have Ethernet?
Once installed, the drivers also had a module which attached to MS Excel, which meant I could start Excel and connect to the DMM and log data directly into Excel. That was
The HP/Agilent 34401A might be a decent choice. Sufficiently modern to be supported by
BenchVue and the older (but completely free)
IntuiLink for DMMs, but old enough to be available used for around $200 if you are patient. Has RS-232 in addition to GPIB, so you do not need GPIB if you only want to control a single meter.
You could use a terminal program like TeraTerm to pass out the GPIB commands to the USB/Arduino/GPIB
TeraTerm will log all the communications (results) into a text file and the you can do a search and replace on the file later, turn it into a CSV file and then get Excel to turn it into a graph.
Many meters can also be set to a talk only mode that will continuously output all readings to GPIB/RS-232. The only thing you need to do is capture it somehow.