You can find official plugins here: Topics tagged official
We (the Discourse team) maintain these plugins, and so they should not cause issues. Official plugins carry the green checkmark you described.
Third party plugins could damage your Discourse instance. In the vast majority of cases, uninstalling the plugin will fix the problem, but this is not always true.
My advice would be to install the bare minimum of plugins, and instead use growing collection of themes in the #theme category. They are much safer to install. You mentioned an image gallery plugin - that can now be achieved with a theme like this: