Recently(ish), I wanted to get the MATE desktop running on my Raspberry Pi. I personally think it looks much better than LXDE, and I didn’t really need the extra performance of LXDE. As with most Debian/Raspbian stuff, it was just a matter of finding the right packages to install. You’ll want to sudo apt-get install mate-desktop-environment xinit. mate-desktop-environment is (obviously) for the MATE desktop, while xinit provides the startx command.