If you the most painless way to go about it, go to vmware.com, download the free VMware Server. Install on your Windows system. Choose whichever distro you want or pick several to try. Create a virtual machine for each and run through the install on each, noting problems or other issues. Work with Linux and put it through its paces. Once you are confortable, you can then move to installing on the physical system.
When you spend all your time working in the virtual world, the answer to every problem is to virtualize!
The first Linux distribution I ever tried was Red Hat Linux 8. (Yes, it was a long time ago.) Not only was it easy to install, but it had lots and lots of programs. I enjoyed it, until I realized how slow it was. It was a slug. It took roughly 10-15 seconds just to open Konqurer.
The next distribution I tried was Ubuntu. This also, I found was slow (and this is my least favorite Linux distrubution, by the way.)
Next, I tried Debian. Debian is one of my favorite distros, because it is "pure" Linux, everything works, and it's very fast. Thumbs up for this one.
After I had tried Slackware, I thought that it was the best ever. It was even faster than Debian, and although you definitely cannot be a Linux newbie when using Slackware, I found that you learn far more about Linux with Slackware than with any other distro. This one's also good.
The latest distribution I am using is Gentoo. I like the fact that everything is compiled, so you get optimal performance, and that you see exactly how a Linux subsystem works (especially if you use the Gentoo Minimal CD). I have 2 servers running Gentoo, and although it's not the fastest to install, and requires a broadband Internet connection while installing, it's my favorite Linux distro to date.
nvidia works good with suse once you get the drivers installed, which is a pain. ati also works good with linux. dreamlinux has an option during installiation that let's install the nvidia drivers easy. sled 10 works extremely well with nvidia cards, so i don't know what your talking about.
and yes 64mb on an old laptop, it's not the fastest thing but it works.
If you're just starting out - looking to indulge into the Linux world, I recommend Mandriva (http://www.mandriva.com). It's got an absolutely amazing graphical installer, and a pretty slick packaging system. It's pretty much what a Linux newbie should use, IMO.
Once they get situated and comfortable mucking around in a shell, and have a half-decent understanding of how Linux/Unix systems are structured (ie. networking, the kernel, etc.), they should perhaps move up to a more...."hardcore"....distro, like Slackware, or even Gentoo (which I'm currently toying around with).
Once I finish up with Gentoo, I'm going to work on installing an OpenSolaris system (my *nix whistle was whet when my dad brought home an old SPARC station running Solaris 4 with the CDE desktop environment - I was about 6 at the time).
Unless I'm mistaken, isn't a P3 i686 architecture?
I'm currently running Mandriva on a P2 450 mHz box, with 160Mb of RAM - and it run's fine. =D
And to further add on to what joeprogrammer is says, distributions "optimized" for i686 architecture processors are all well and good, but if you're going for speed, a distro like Debian - which uses an i386 optimized kernel - is slicker than snot on a doorknob. I've actually been hard-pressed to find a distro that's as "speedy" as Debian.