"LXDE" is a really svelt Linux GUI
I'm not claiming it's the smallest (it's not) or even the fastest or the best, but it is pretty good for my needs, on my 12 year old celeron computer in my back porch farm office/dog room/Ham radio shack. It only has 576 megs of ram. The computer is too old to spend money on buying more memory, so I wanted an operating system that would use a minimum of system resources. I chose PCLOS Linux, using the LXDE gui (graphical user interface), and it's made a big difference.
The minimum RAM requirements for LXDE is 384 megs. I was using Linux Mint GNOME on the computer before this, and it's minimum RAM requirement was 512 MB. It worked ok, but was a bit slow and clunky; I had to wait a lot, and could not multi-task much. Thus, using the computer had a slight "painful" quality.
With this new install with LXDE, things are considerably faster, and I can multitask a bit more. It's a lot like having a "newer" machine.
Now I know there are other GUI's that are smaller and faster. I've tried many of them. But in general, I've found that they have a lot of ... "rough edges".