If you wish to run a graphical program like Firefox, then you need to be running X windows.
The SERVER can be in "init 3" (no graphics), but you can run Firefox remotely (by using vncserver, or by using an X emulator and setting $DISPLAY on your remote PC).
Conversely, your server can be in "init 5" (graphics mode) ... but if you <Ctl-Alt-F1> to a text-only virtual console, then you CANNOT run Firefox (because your logon console has no graphics).
Bottom line: if you're sitting in front of an X Windows logon, then you can run Firefox (whether your X windows is local or remote). If you're sitting in front of a text-only logon, then you can't.
It's as simple as that