How can I emulate keyboard and mouse commands with a game controller?
xPadder
You've stated you're interested in xpadder, which I highly recommend. I've used it and it works wonderfully; it has a great user interface and makes setting up a controller a breeze.
Easy configuration
The ability to import a picture of your controller and configure each button in the right place on-screen makes it really, really easy to configure. You can see exactly what you're doing.
No configuration
Usually, though, you won't have to configure anything, unless you have a really, really obscure controller and/or really, really obscure game. You can simply google e.g. "xpadder mass effect" or "xpadder bioshock 2" or "xpadder 360 controller" to find controller images, controller config files, and game config files already carefully created by somebody else to work with your controller and the default key/mouse settings for your game.
Powerful
There are a huge amount of useful options for what each button can do, including all possible key combinations and sequences, mouse movements, etc
Free version
If you want to try xpadder before buying it, you're in luck. There exists an older version (v5.3) that the author has stated will remain free because it was the last release that supported Windows 2000. (Source)
However, it is over two years old (came out in 2008 I believe), so it will not have any of the bug fixes or some controller support that xpadder has gotten over the last couple of years.
You can download it here.
AutoHotkey is a fantastic program that will meet most of your needs. It takes a little bit of effort to understand how it works, but once you do it can be insanely powerful. It has support to map up to 32 joystick/gamepad buttons, as well as the POV controls and XY axes. You can even set it up to target a specific gamepad or joystick if you have more than one connected to your computer.
Unfortunately, it doesn't meet all of your criteria (easy to setup), but the power it gives is worth the setup time. It has worked for every game I have tried.