Automatically make QuickTime fullscreen when opened
QuickTime Player doesn't have a Preferences... menu command like other applications do, nor does it have a com.apple.quicktime.plist file to manipulate. Therefore there isn't anything you can do directly, however here is a workaround of sorts.

Note that this workaround requires changing the default application for file types, e.g. .mov, you'd normally open directly with QuickTime Player to the application created herein, called: QTP Full Screen.app

Using Automator create a new Application and add a Run Shell Script Action.

Change: Pass input: [to stdin] to [as argument]

Add the following code:

if [[ ! -z $1 ]]; then

    open -a "QuickTime Player" "$1"

    osascript -e 'tell application "QuickTime Player" to activate' \
              -e 'delay 1.5' \
              -e 'tell application "System Events" to keystroke "f" using command down' \
              -e 'delay 1.5' \
              -e 'tell application "QuickTime Player" to play front document'
fi




Save it as an Application named: QTP Full Screen

In order for QTP Full Screen to be the global default app for, e.g. .mov, files you'd open in QuickTime Player you'll have to use the Default Apps Preference Pane, RCDefaultApp by Rubicode to change which application opens a given Extension.

Install RCDefaultApp and then in System Preferences > Default Apps select the Extensions tab and scroll down to mov and then change the Default Application: to: QTP Full Screen

Now then you double-click .mov files in Finder or accessing them from Spotlight the QTP Full Screen application will open the target file in Quick Time Player, set View to Full Screen and start playing the file.

Note: If you do not want it to automatically start playing the file then remove the line of code, the one that has "play front document" in it.

If you need modify other default methods of file types, Apps, URLs, UTIs, etc. the Default Apps Preference Pane, RCDefaultApp by Rubicode, is a great utility for it.

To make the QTP Full Screen.app application bundle look better in the Applications folder you can copy and paste the QuickTime Player.app application icon from its Get Info sheet to the icon of the Get Info sheet for QTP Full Screen.app.

Note:  The value of the delay statements can be adjusted in seconds and or decimal fractions thereof, as might be necessary on any given system to account for its processing speed.