Okay, where to begin?
Well there are tons of distributions out there, some hold your hand through the installation process via whizzy point and click GUI's in a similar vein to installing M$-windows (e.g. Fedora, the Ubuntu family) whilst others throw you straight in at the command line to do everything (e.g. slackware, Gentoo etc.).
If you want to get started the best thing to do would be to grab a live CD image and burn it to CD, then reboot your computer and boot from that CD. It will load everything into RAM and run on the fly, it won't destroy your current installation, but will give you an idea of what things are like. Recommendations on this would be to use XUbuntu (
http://www.xubuntu.org/) or Knoppix (
http://www.knoppix.org/) with the fluxbox window manager, or Slax (
http://www.slax.org/). More on this bellow.
The partition thing is a very sensible way of dividing up your hard drive so that files and programs that are involved in actually running the operating system are kept in one place (this will be your 'root' partition and is denoted by the location '/'). You then traditionally have a 'swap' partition which is used as an additional area when the RAM requirements exceed those provided by your hardware (in a similar manner to M$-windows page-file system or whatever its called), this will normally be double the amount of RAM you have installed, but you can add more. Its then normal to keep your user files (all your music, videos, letters etc. etc.) on a separate partition so that should your installation become unstable, need re-installing or you wish to try out a different distribution you don't need to move everything to an external back-up, you would just install to the root partition.
Now, the beauty of Linux is that its very modular, which in turn means there are lots of choices to be made as to which modules to use. Your likely to want to have a desktop to use for doing everything, and your system hardware isn't that powerful, so you want to keep things light-weight so that your operating system thats providing your desktop and so forth isn't hogging resources and slowing the computer down. There are a wealth of desktop environments to choose from, but the common thing to all of them is that they are all run on an X server that does all the clever communication between your graphics card, and HID's (Human Interface Devices such as mouse, keyboard, monitor). Anyway, you want a light-weight desktop to run things. The two most popular desktops are GNOME and KDE, but these are now getting rather bloated, so I'd recommend Xfce (which is the default with Xubuntu) and its Gnome basedd so you will have the necessary libraries for installing other Gnome applications or if your system is labouring with this you could try fluxbox which is even lighter (but note that you won't have icons on your desktop without running some additional applications). Again part of the beauty is that its very easy to install and try one of these out and if you don't like it remove it and try something else.
You'll find that Firefox is also a bit of a resource hog, so might want to look at using an alternative (personally I use Galeon which is Gnome based annd uses the gecko engine that underlies mozila firefox).
Other things you are likely to want to do are word-processing in which case you can install OpenOffice, email (tons of options including thunderbird from mozilla, evoluation, and my preference claws-mail), picture manipulation (go with GIMP, but other useful things include hugin, f-spot and many others), if you've an iPod then you can use gtkpod to get things working without too much hassle, but other USB mp3 players are even easier to work with as there is no attempts to obfuscate their internal workings and they will generally mount as external HD's/USB pen-drives, as should most cameras.
If your completely unsure I'd highly recommend Xubuntu, recently installed on my wife's aging Vaio and its breathed new life into it as the wireless network card was rather flakey. You should find that all of your hardware is detected and works without any problems.
It would be worth upping the RAM, and its highly likely that this is possible, what you'll find is that there are currently two 128Mb chips inserted on your motherboard, these can be taken out (obviously when the computers switched off and you've earthed yourself, to avoid blowing the motherboard through static) and replaced with chips that carry more RAM, sticking 2Gb in would be a good idea, and not too expensive.
You'll find that the forums for Ubuntu are very friendly and useful, but be prepared to provide information when requested and to read (well-written) HowTos, it takes a while to get your head round things, but it will slowly come together.
One very important thing though is user-levels/rights. During installation you have to set up at least one user this is known as 'root' who has permission to do absolutely anything on the system, install and remove software, delete things, insert malicious code, turn your computer into a server selling pr0n. You then have a user account for day to day work, who has very limited rights to install and remove things (basically none). This is a very sensible and purposeful design and something that was neglected by M$-windows and has consequently resulted in the proliferation of malware/virus'/trojans etc. Never log into your system as root, if your using Xubuntu, then you will do everything via 'sudo' or will be asked for your password each time you want to do something that only root has the rights to do.
Anyway, rather waffly, and a bit all over the place, will dig out some links in a bit on useful overview and sites.
One to get you started is the above Xubuntu site, and also
http://www.linuxquestions.org/slack
