So the question is when is it appropriate to use each system, backtick, or other modules? Is there best practice?

See my take on pretty much that exact question here: Calling External Commands More Safely.

Basically, I would almost always recommend using a module over system and especially backticks, for the reasons I describe there. I usually recommend IPC::System::Simple's systemx and capturex, or if you want control over STDIN and STDERR as well, IPC::Run3.