Firstly, Linux is NOT an OS.
Linux is a kernel, that operates at the heart of an OS, that tends to be called Linux. There's certainly a lot of confusion here (the above link points to the kernel's website, for example).
GNU/Linux (the OS using Linux), is very good for a lot of things.
1) Principle of free software (free as in freedom, not beer). It's your computer, you should be able to modify it to do what you want. Just as the engine in your car is yours, so if you want to modify it, you should be able to in principle. This is the central idea.
2) You can make it quite heavy with lots of graphic effects, or very light. It's up to you.
3) There's really far more to talk about than in an answer here.
4) You can try GNU/Linux out straight from a CD, without installing to your hard drive. Try ubuntu from ubuntu.com. It's a free download to get the CD image, and then you can try it out on your current PC. Take the disc out again, restart, and you're back into Windows with nothing changed.
BTW, Asus put Xandros onto their machines. It's a distribution of GNU/Linux, much like Ubuntu. And it's really not too bad. But there are nicer alternatives out there, that are pretty easy to install. You might want to try eeeUbuntu, for example, if you get an Eee Pc.