Emacs with Linux mint: how to set up emacsclient

[djc]

On Linux mint (18.1 MATE) I've installed emacs 24.5.1 using the software 
manager. Now the "Open With" menu lists

    GNU Emacs 24 (GUI)
    GNU Emacs 24 (Terminal)

and I've set some file extensions to be associated with Emacs (GUI) by default. 
But what I'd really like is to do everything through emacsclient and get rid of 
those two entries. I'd guess I'm not the only person who prefers things this 
way.

Can you explain to me how to do this? That is, remove those two entries, add a 
single one for emacsclient, and associate certain types of files with 
emacsclient?

Thanks!