I think of LXDE and Mate as lightweight; both work well for me on my 6-year old netbook (32-bit Atom N270, 1GB RAM). I haven't tried running XFCE for a while, but I've also run it on the netbook in the past without issue. The nice thing about LXDE is the very limited tie-in among the component DE apps. However, this results in a less-unified look and feel. Both XFCE and Mate present a more unified collection of default components, at the expense of more a bit more required CPU horsepower. My advice is pick one, try it, and if you don't like it, try another until you find one you like. Unless you're looking at a Celeron-based laptop or Chromebook, you shouldn't have any trouble running any of the popular desktop environments, including Gnome, Unity, and KDE.
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