I have several custom Themes and Plugins that I have written that I would like to start testing under the forthcoming WordPress 5.0 / Gutenberg version. How would I go about doing this? Just install the Gutenberg plugin? Or perhaps download the nightly build and install that in a fresh install?
You don't need the nightly build unless you're looking for deeper core compatibility issues.
For strict Gutenberg compatibility, the plugin itself should be sufficient as long as you keep it updated.
You can do the nightlies on a fresh install if you wish, but it's unnecessary overkill IMO.
I would (and do) unit testing with just the Gutenberg plugin. I would then do core updates as RC's come out and then do a final round of testing with the release version of 5.0.