On the one hand, KDE is a classic desktop, with an ecosystem of applications that only GNOME comes close to rivaling. Unlike GNOME apps, KDE's have neither a consistent interface nor a highly organized one, but most of them have more features and options you have ever seen on a desktop without opening a terminal.
Some users find the array of features so overwhelming that they are only confused. Others, even if they decide against the KDE desktop, still install its libraries so they can use apps like the Amarok music player, the K3B disk burner, or the digiKam photo manager.
On the other hand, for the last four years, KDE has been doing more experiments with the desktop than any has other desktop project. Panels, menus, and desktop icons -- all the elements users are conditioned to expect -- are still a part of KDE, but they have been rearranged as KDE reorganized its back end into a series of subsystems.
Even more confusingly, the traditional elements have been extended by a series of features, ranging from hot spots on the edges of the screen to a library of special effects and tools that encourage task-oriented organization, and multiple icon sets. Many KDE users never use these extended features, but ignoring them altogether can be like holding a conversation while pretending to ignore a ghost that has dropped by for a haunting: they leave some users edgy and bewildered.
In addition, KDE has what might be called an anti-cloud approach. Instead of encouraging you to do everything in a web browser, KDE has opted for widgets that incorporate online services directly into the desktop.
All KDE's features make high demands on memory, so you probably don't want to use it with less than two megabytes of memory. But if you have the hardware and the temperament, KDE is an all-purpose choice with features for users of all levels of experience.
LXDE (Lightweight X11 Desktop Environment) is a reaction to the perceived bloat of desktops like KDE or GNOME. Its home page claims that it runs well on computers manufactured as far back as 1999, and it is definitely faster than most of the desktops described in this article.
However, while most lightweight desktops look antiquated or are so pared down that they seem crippled, LXDE looks modern and simply minimalistic. If you compare its customization options to a major desktop's, you will notice that LXDE offers the choices that users are most likely to want -- and absolutely nothing more. In this sense it is similar to Xfce, although it is faster than some implementations of Xfce, Xubuntu in particular.
Mate is Linux Mint's fork of the GNOME 2 code.
Like the complementary Cinnamon, Mate is a recent option, developed and maintained for GNOME users who dislike GNOME 3. However, given the simplicity of GNOME 2, it might be recommended equally strongly for new users.
At a glance, Mate is obviously not Windows 7. However, a few minutes of exploration reveals that both are minor variations on the traditional desk. The features look different, but on both the functionality is almost identical.
If Mate were a car, it would be a Honda Civic or Toyota Corolla. It's so ordinary that teenagers wouldn't take it for a joyride, but it's dependable and gets the job done.
In other words, anyone who prefers to focus on applications rather the desktop will probably appreciate Mate. If for some reason they don't, then Trinity or Xfce might appeal to them.
Trinity is a fork of the KDE 3 release series, designed to modernize it and keep it alive. To some eyes, it might look old-fashioned, like a video game designed for another era in which video cards were less advanced. To others, it is a piece of classic design in which form and function were united in a way they rarely are today.
The main drawback to Trinity is that it is built by only a handful of developers, who are trying to nurse software whose design -- and, for all anyone knows, its code as well -- is over a decade old. At the same time, the developers are trying to modernize it and keep it current. These are demanding tasks, and in the past Trinity's quality control has not been as high as it might be. Wisely, however, the project has decided not to hold to a fixed release cycle, opting only to release when ready.
If Trinity seems not quite right for you or a person you are advising, you might look at Cinnamon, Mate, or Xfce as an alternative.
Unity is Ubuntu's interface for GNOME. Its design is based heavily on the constraints of mobile interfaces, although its memory requirements are by no means light. Signs of this influence include a fixed panel, and the replacement of the traditional menu with the dash, a series of filtered views of installed applications that occupy the entire screen.
Like mobile interfaces, Unity is easy to learn. However, navigation is not always efficient. Frequently, Unity frequently require several more mouse-clicks than other desktops to perform the same function. Administration and customization functions especially tend to be buried deep in Unity, although the filtered views on the dash can make them somewhat easier to find.