How could I start a Selenium browser (like Firefox) minimized? I want the command browser.start(mySettings) to start a browser minimized.
Your question does not say that why you want to run your test cases in minimized browser but unfortunately selenium do not provide any built-in function for the same.
Normally when we want to run test cases with maximized browser we use driver.manage().window().maximize();
No doubt there are several ways to minimize your window through code by using Java key event by using keyboard shortcuts for minimimzing window or by using JavaScriptExecuter but that too depend on which OS and language you are working.
One more thing you can try is HtmlUnitDriver.By using this you cant even see the browser, so that may also serve your purpose if you have a case of not opening the browser while execution of test cases.