I have one machine that has 256 MB of RAM and Mint 6 runs just fine on it. However, the GNOME Live CD was slow as syrup. I took my Mint 5 Xfce Live CD, used the partition editor to set up my partitions and give a /swap file for Mint 6 to use. I switched discs, booted Mint 6, and I was able to install without difficulty. This machine is only used for email and web browsing, so the amount of RAM + GNOME has not been a problem.
Now, the Xfce version of Mint is much lighter weight, as well as the Fluxbox version being even lighter, I do believe. All of these versions benefit from Mint underneath, but with different desktops. Those may be a better fit with your hardware. You may wish to test them out and see what you think.