I have a similar but dual core Atom netbook. The thing I did was put an SSD into it, and then installing bare Debian. I chose no graphical system from the installer. From there I installed i3 as the window manager and launched it with an automatic login script checking if I was on TTY1.
That’s all I did, basically keeping the stuff the little thing has to run to an absolute minimum, and a fully fledged desktop environment would have set it on fire.