How can I change Blender from the default cube/lamp/camera default setup? Also, is it possible to change other features, such as the default view direction (Top, Side, etc) or the Editor type (3D View, Node Editor, Graph Editor, etc)?
File > Defaults > Save Startup File (also bound to Ctrl + U in the 2.7x keymap) will save your current settings and setup as the default startup view, meaning it will set everything as the default including the current view(s), whatever data is loaded (images, models), and the User Interface. This overrides the startup .blend file found in the config folder and can be used on another machine or similar version of Blender.
You can revert back to the factory defaults at any time by using File > Defaults > Load Factory Settings.