How Can I Start a Program Minimised, and Restore Maximised?

You can achieve a minimized maximized window using Python:

import wnck
import gtk
import subprocess
import time

chrome = subprocess.Popen(["google-chrome"])

b = True
while b:
    screen = wnck.screen_get_default()
    while gtk.events_pending():
        gtk.main_iteration()
    windows = screen.get_windows()
    for w in windows:
        if w.get_pid() == chrome.pid:
            w.maximize()
            w.minimize()
            b = False
    time.sleep(1)


chrome.wait()

google-chrome in this case will maximize then minimize. After this you just create a .desktop that can launch the script like the example shown below:

[Desktop Entry]
Version=1.0
Type=Application
Name=Application Name
Comment=Application Comment
Exec=python /exact/path/to/python/script.py
Icon=icon
Categories=valid categories;

Make sure to set the desktop as a executable file or it will not function.

The script should be edited on line 6 where google-chrome should be replaced with whatever command you wish to execute. If the program have parameters they can be passed as following: "google-chrome", "para1", "para2".

Cred to this question for the python script (changed to chrome in my testing).