Of these four ways, what is the best way to capture volatile memory comprehensively from a running machine for forensic purposes?

1. FTK Imager
2. memdump -k
3. dd if=/dev/mem . . .
4. LiME, or other kernel module capture utility?

I don't do much in terms of forensics but FTK is used by professionals. And is free.
Some times the hard work, if it would be used in court, would be to prove the evidence is valid and nothing was altered by the analyst or the tool.
And of course if the tool represents the truth.

I am not sure if it would be done using a firewire port or so, today, so you don't have to execute it on the box itself, as it would inherently change the memory you are trying to dump.
If you can find a tool listing for the SANS 500 or 508 class you would be on the right path.

I dont know LiME unfortunately.

https://www.sans.org/cyber-security-...ting-training/
https://www.sans.org/cyber-security-...nsic-analysis/
I am not sure if the links are useful but have a look.