Welcome to the forums!
Asus made several different models beginning with the number 1000; it would be helpful if you could tell us your hardware specs so we can make a recommendation.
Assuming your hardware meets the minimum requirements, I recommend you try Linux Mint, which is currently the most popular Linux distro for beginners. If the default Gnome environment is too "heavy" for your system then you can try a "lightweight" desktop environment such as LXDE or Xfce. You could also try Ubuntu, PCLinuxOS, or Puppy, which are all very popular with beginners.
Keep in mind that software cannot change your hardware. If you have a slow computer, and XP runs slowly on your slow computer, then Linux will probably also run slowly on your slow computer.
However there may be some performance tips/tweaks we can offer once you have the basic system up and running.
ps There is an excellent eee-1000-specific subforum at http://forum.eeeuser.com
unfortunately the site is down for maintenance right now.