To my mind the wrong question is being asked. “What desktop enviornment for an old machine for speed?” is kinda meaningless – unless we're talking a Pentium 75, and/or you have a specific need for maximum speed.
The real question, I hold, is... what will the machine be used for? That and, how do you like to work?
I am a KDE fan. Arguably it is not the fastest GUI for Linux – though, yes, it has been dramatically optimised and once effects are turned off runs fine even on slower hardware. My wife is happily running Mint 13 KDE on a single core Atom n455 which benchmarks slower than a Pentium 3 and she is delighted with the sheer raw speed. No seriously. She raves about how fast it is. This is compared to a badly snarled up Windows machine mind.
For general office type operations you are not going to see much difference between an older machine and a new, faster one. I mean, how much power do you need these days to run a wordprocessor?
When I was working in the WHITE HEAT of a Singapore based International school (18 hours a day, 7 days a weak much of it taken up with mindless paperwork with impossible deadlines) I had to work and work and work. My netbooks were vital to me in this tme. I had two I was using – my Atom and more a powerful Celeron.
Now, for processing tasks such as OCR or larger image processing, yeah, there was a big difference between the atom and the celeron. But for 90% of my work; producing documents, printing, web use, playing videos, creating presentations, producing more meaningless documents... the two machines ran at virtually the same rate. I actually standardised on the atom because it was smaller and had a much better touchpad. (The Acer Aspire One 756 - nice machine but ruddy awful touchpad!) The physical interface (touchpad) was more important to me than processing speed.
Note also: I use Kdeline for video editing quite a bit. I tested rendering time under KDE and then under LXDE on my Celeron recently. Absolutely no difference. Not one second was gained in render time using a lightweight GUI. (OK, with desktop effects on in KDE there is a big difference for everything but that's desktop effects on minimal hardware.)
I use KDE not for speed but because KDE works the way that I work. MATE does seem faster than KDE, I'll grant, especially on start up Mate loses me time in fiddling around in, what is for me, an unintuitive system. Conversely, KDE's keyboard shortcut assignment system was a life saver at the Singaporian school and now I can't live without it.
Now, I am not saying that MATE, or Cinnamon or LXDE or whatever are bad GUI's – it's just that KDE works in a way that _I_, personally, can understand. Others are different. But frankly, a P4 with 1GB of RAM will run any GUI really sans desktop effects and you're way beyond that. I am typing this on an 8 year old Turion laptop with 1.5GB of RAM. Oh look, it's running KDE and is quite fast enough.
So... you can run any GUI you like on your machine. Now you need to answer these questions:
1) What do you want to do with the machine?
2) What GUI suits your style of work? If you like KDE, go for it! Who cares about the occasional 1 second delay, maybe, between KDE and, say, Mate when running up GIMP?
3) Who will be using the machine? I assume you and, therefore, you can run what you like. But if you will have your grandparents running it then maybe you're better off just putting on Zorin and being done with it?
I tell ya, do not go for the fastest of the fast. It's far better to spend a little more time enjoying your Linux experience than gaining a seconds worth of processing but losing five minutes while you hunt down how to change a 'Start' menu item or find you have to install an app to change screen colours (if it matters to you – it does to me.)
Make the machine fun! Make it work for you and don't sweat the speed. Whatever you go for, the desktop enviornment will be faster than Windows and that's fast enough, and your hardware is far from minimal. A single core atom or an AMD C processor or a Pentium 4... those are minimal!
Enjoyment is better than optimisation. Hell, if optimisation was the source of all computing happiness we'd all run Gentoo or Sourceror! Have fun!