If you forward the display with ssh -Y, the setting of variables is all done for you automatically.
eg:
zsh-% ssh -Y wgscott@my.linux.machine
linux.machine-% echo $DISPLAY
localhost:10.0
If you decide to use "nomachine" you need the server software on the remote linux machine, and client software on your mac. Then you can run the whole windowing environment from the linux machine painlessly. It works a lot like vnc, except for whatever reason is much faster and the rendering quality is much better. It took me about a year to try it from when it was recommended to me, because I scoffed at it. I was wrong.