I suggest Q4OS (with Trinity DE). It loads itself at 340 MB of RAM, so it leaves you with a lot of free RAM (especially since the heaviest apps now are browsers -- youtube needs 1 GB for itself). Arch Linux with XFCE can be made to boot at 470 MB. Debian starts at 650 MB. Ubuntu/Fedora start at over 1.5 GB so avoid.
Then of course there are the damnsmalllinux, antix etc, but the user experience on these is bad. Q4OS feels like a modern OS with GUI panels for everything, while not taking lots of ram.