That is a really small amount of RAM. Without considering the GUI, it does not really matter which distro you choose -- a console based system is a console based system and it will run on that.
But with regard to a GUI desktop, you are going to want to go as light as possible. This is about the Desktop Environment (DE) and Window Manager (WM) not the distrobution. However, different distributions use different DEs and WMs by default (but you can change them).
There looks to be a great comparison of this stuff including RAM usage here:
Not surprisingly, GNOME, Unity, KDE, Cinnamon (the default on mint) are out. Maybe so too is XFCE. LDXE seems the best choice, DE wise.
The lightest way to go is to just run a window manager without a DE; on the table 3/4 of the way down that page, everything from OpenBox on down is a stand-alone WM. These don't have all the features of a DE and may require more work on your part WRT configuration. However, they do have all the important features. My all time fav setup involves FVWM, another very lightweight highly configurable WM. The only reason I'm using KDE right now is because it looks cooler, lol, but for flexibility, FVWM wins hands down.
So if you are new to linux, try LDXE at first but then try and learn how to use one of the stand-alone WMs: LDXE uses a third the memory of (eg) KDE, but (eg) Fluxbox uses half that again. Lubuntu 12.04 appears to have a LDXE option, probably somewhere in the install process:
That would be my recommendation.
Then: good luck running a browser, lol. Raspberry Pi distros use midori; I haven't used it much but it seems to work nicely and I am sure will be in the lubuntu repository. The pi has 512 MB tho.