Mandrake 9.2 (you can download it for free) should be able to partition your drive and install itself quite easily. I'm a newbie, and this is the easiest distro I've found.
I'm running it just fine on a laptop with specs similar to those of your machine, so there shouldn't be any problem with disk space or RAM requirements.
If your laptop currently has Windows 98 or ME, it probably uses the FAT32 file system. That means you have to defragment it before you partition it, otherwise files could be taking up bits of disk space all over the place. You'll have to defrag it manually in Windows, there should be a utility in your Start menu somewhere.
Fortunately, Linux is much more advanced, and doesn't have fragmentation problems.