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 Fit to 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' \
-e 'tell application "System Events" to keystroke "3" using command down' \
-e 'tell application "QuickTime Player" to play front document'
Save it as an Application named: QTP Fit to Screen
In order for QTP Fit to 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 Fit to Screen
Now then you double-click .mov files in Finder or accessing them from Spotlight the QTP Fit to Screen application will open the target file in Quick Time Player, set View to Fit to 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 Fit to 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 Fit to Screen.app.
Note: I added the
if statement to the code so the QTP Fit to Screen application doesn't error out when executed by itself. In other words, double-clicking it will essentially do nothing, whereas without it will throw a couple of error messages.