Was using Crunchbang and installed Bunsenlabs Hydrogen few weeks back. Its the community fork of Crunchbang - http://www.bunsenlabs.org/
I have this on Asus netbook which I use once in a while and also have the 64bit version on my desktop. Have been using since 2013 and can say that it just lets me do what I want. Simple UI and debian stability.
I think any version of Linux you try will be fast enough. You'll have to choose a desktop environment that's lightweight, and only install the packages you need.
Download any major distro - Debian/Fedora/SUSE, and try out KDE/GNOME/XFCE/MATE/Cinnamon/Enlightenment.
Choose the one you like best, and uninstall the rest.
I have installed Linux Mint 17.3 with Cinnamon. Everything seems to be good except for Youtube. Playing Youtube via Chrome or Firefox the video is very choppy. The CPU is at 100%. My configuration is: 2 GB DDR2 RAM on a AMD Neo MV-40 64 bit processor http://www.notebookcheck.net/AMD-Athlon-Neo-MV-40-Notebook-Processor.35096.0.html.
Please suggest if there is anything that can be done to improve Youtube playback?