You're only running 512MB of memory, which is pretty low for Windows XP these days. While 512 will do, 1GB is pretty much standard (and 2GB is slowly creeping up).
You will probably see a decent performance increase just by adding another 512MB of memory, though it may or may not make a huge difference. A combination of more memory and a dual core processor would give you the biggest performance increase; however, that would also require you to buy quite a few new components.
The way I see it, you can go four different routes:
#1 - Buy more memory and call it a day. This will be the cheapest option, but definately give you the least performance gain. If your computer is only seeming a little bit slow (mainly when opening applications, or if you have multiple windows open), this is probably plenty. Keep in mind, you will most likely be throwing your money away when you consider the future.
#2 - See if your motherboard will handle a cheap dual core (Pentium D, Prescott 800 series or Cedar Mill 900 series), and add some extra memory. This will cost a bit more than the previous option, but also increase performance by quite a bit more. Having a second core really does help, even if you're just surfing the web, listening to music, and burning a CD all at the same time. Careful though, the Pentium D's, ESPECIALLY the 800 series, run very hot. Again, this would basically be throwing money away.
#3 - Buy a used, older dual core setup, such as an AMD socket 939 rig. You may know someone, or be able to find someone with an older X2 3800+ or Opteron 165 and motherboard combo that wants to sell it at a reasonable price. This would let you reuse your memory and (hopefully) graphics card, while still gaining a significant performance increase. You would still have to upgrade to 1GB or so of memory to get the best boost. This would probably be the hardest option to work out (unless you just happen to know someone), so I don't really suggest it.
#4 - Complete system upgrade. If you can afford it, go with a dual core Core 2 Duo or AMD X2 AM2 system. Plan on at least 1GB of memory, a low-mid range graphics card (7600GT, X1600, etc., or even lower if you're 100% sure you'll never touch a 3D game), and an entry-level dual core processor, such as the Core 2 Duo E4300. You're going to spend $400-500 or so in the end, but it will be money well spent.
Overall, it really depends on your budget. If money is tight, go with option 1. If money is sort of tight, and you REALLY want to reuse most of what you have, look into option 2. If you have a friend looking to unload a slightly dated system, check out option 3. If you can afford a new upgrade, treat yourself... you'll love it.