The differences between hardware and software calibration have become blurred during the course of this thread.
Software calibration typically means using an app to change the colours on the screen and then using your eyes to determine what is correct (Mac OS X has such an app built in) - System Preferences/Displays/Color tab/Calibrate. All I can say is that it is better than nothing...
Hardware calibration typically means using a hardware colorimeter such as a Color Munki, Spyder 4 etc. to calibrate the monitor, along with a compatible software app - far, far superior to the software/eye solution built into OS X and I would guess is what the majority of graphics pros around the world will use to calibrate their screens. Effectively this is a hardware+software solution and works on any computer+monitor combination (as long as the software is compatible with the OS). In this thread this has started to be called software calibration for comparison sakes with the built in hardware calibration in the Dell screen. So yes, you can hardware calibrate a u2413 on a Mac using this solution.
Another type of hardware calibration is the one found in the Dell monitor. This is built into the screen itself, so cannot be used to calibrate a different screen. This solution still requires a colorimeter, and as the Dell monitor demonstrates, the colorimeter must be compatible with the screen hardware too.
Hope that helps clear things up.
These are worth considering as alternatives to Photoshop, and are free or very cheap:
Gimp:
http://gimp.lisanet.de/Website/Download.html
Pixelmator: search the Mac app store. It has great reviews and costs £10.49
I've never used either though, but they certainly look very good and have good reviews.
Photoshop Elements - affordable, but more expensive than the above programs. Although not identical, it will give you a reasonable grounding in the interface for the full version of Photoshop, should you ever upgrade to it.
Lightroom/Aperture
I prefer Aperture. As others have said, I prefer the user interface and you really can do a lot in the program - I do entire wedding edits using it, only going to Photoshop for heavy duty retouching (if required) or opening of closed eyes in a group shot! I'm guessing Aperture will be updated when the new Mac Pros are launched.
Lightroom is equally capable as Aperture (people will argue over which is the better program - I think they are both excellent so use the one you prefer using, and one or the other may have what you deem an essential feature which the other is missing - lens correction in Lightroom for example, which is something I don't use but some people use all the time), but I too find the interface less intuitive compared to Aperture.