Your biggest limiting factor is your ram. Ram will prevent you from checking out the Live CD's and from using even some of the lesser-featured distros. If you can find a stick for that empty slot, that'll open up a few more options. You also need to find out if your system will boot from CD. If not, then you'll need to create a boot diskette. Don't worry, there are plenty of sources on the internet for those. All this aside, there are some distributions that would likely work nicely on your rig as it is.
The first distro that comes to mind is
DSL (Damn Small Linux). DSL was one of the very first small footprint distros.and they keep improving that niche with every release. Coming up in DSL's rear-view mirror is
Puppy Linux. Puppy linux is beginning to win over a lot of users. Even users with powerful rigs seem to admire the beauty and economy of this tiny distro. And speaking of tiny... Tiny Linux weighs in at a petite 57MB, requires 50 MB disk space (80 recommended), 8MB ram (but works better with 12 or 16) and
requires a floppy drive. This is a very spartan distro though. In this category there is also
Feather Linux which is one of my favorites in this bunch. And I would be remiss if I didn't at least mention SLAX. Slax is based on Slackware, the oldest living Linux meta-distribution on the planet. I've never tried SLAX, but it does fit within your hardware profile.
Another distro, which is a step up in features and function is
Vector Linux. The system requirements are a notch above the ones I've mentioned, but they are still within your profile. Vector does a good job of adding features in an intelligent design without making great sacrifices of speed. Finally, there is Xubuntu. Xubuntu wouldn't really be a good option for you unless you filled that empty ram slot. The bare minimum Xubuntu will run on is 64MB ram, but it really needs 128MB to function in an acceptable manner. If you can swing that though, Xubuntu is really one of the best choices for a MS Windows user who wants to try out linux on a machine with limited capabilities.
I hope some of this helps. I heartily recommend you burn copies of at least 3 or 4 distros and check them all out. Remember as you embark on your journey, that " a GUI does not an OS make". There are several window managers and desktop environments for linux. You will be limited somewhat in that regard by this rig, but if you find you like linux and decide to install it on something with a little more umpff!, you will be pleasantly surprised. The latest incarnation of KDE (4.1.2) is a thing of beauty. Infinitely configurable to your preferences, and every bit as beautiful as Mac OSX or Vista. Linux coders have traditionally shunned flash in favor of function and stability, but this time it looks like they're going for all three. And on a Core 2 or Athlon64 system, you shouldn't see any speed penalty.
Before I wrap this post up, let me make one last recommendation. Download and burn a copy of Parted Magic. This is a bootable utility disk that can get you out of all kinds of jams and generally make life easier, whether you're using Linux or Windows. OK, that's it. I leave you to your choices. Don't forget to take time to savor the experience.
Peace!
CloudCutter