As of early 2021, the previously accepted answer is no longer the case. Emacs can now be ran in Wayland without XWayland. Core Emacs code has been (quite labouriously!) updated to use pure GTK, and this should be available to the general public as of Emacs 28. For now, Arch Linux users can use the updated Emacs by switching to this AUR package. Other ...
If you forward X11 you need Lucid emacs, because gtk emacs may crash if the ssh connection is lost and X server crashes.
Note the error message when trying to run emacs --daemon with gtk emacs
$ emacs --daemon
Warning: due to a long standing Gtk+ bug
Emacs might crash when run in daemon mode and the X11 ...
Daemon mode is THE preferred way of running emacs (numerous benefits), but the almost certain crash in the event of disconnect from the display is weighing in favour of the Lucid toolkit instead of Gtk.
Note that this happens on local instances also, i.e. you don't have to forward X11 for it to happen. Just start emacs in daemon mode, fire up an emacs frame ...
With a sun keyboard, for me, it works quite straight forward.
(global-set-key (kbd "<XF86Paste>") 'yank)
(global-set-key (kbd "<XF86Copy>") 'kill-ring-save)
(global-set-key (kbd "<XF86Cut>") 'kill-region)
For the terminal integration, that's related to the OS itself and how it manage the keyboard input, this ...