Customize Preview (easy)
Have you looked under Preview preferences? You can set Initial Document Scale to 100% or larger if you want. You might need to adjust the option below that, defining size equal to screen or print sizes.
Use a better PDF viewer
If Preview.app can't do what you want, look into Skim.app
Skim has an option to open PDFs as Default, Maximized, or Fit. One of these ought to improve.
Customize Preview (complex)
If you want all three points requested above and want them in Preview.app, I would do the following:
- Turn on Universal Access so you can script applications via the GUI
- Make a new app in Automator that accepts PDFs. Replace Preview with this (open with this by default, put it in your dock so you can drag-and-drop onto it, etc.)
- The new app should simply take the input PDF and pass it to Preview, so it displays there
- The new app should then use Universal Access commands to
- Maximize the window
- Set to "Single Continuous Page"
- Select the mouse tool you want.