Once again, I agree with pp2's sound advice. His suggested card with more on-board RAM is a better choice. The more capable the card, the better the performance and the more tasks the CPU can hand off to it. But you should look at your PSU sooner rather than later. You need to ensure you have adequate power installed before
you install hardware that demands more power.
The new card will certainly improve over all computing performance as computing today is very graphics intensive. Installing a card will also free up that little bit (8Mb) of system RAM currently used by the integrated graphics, in effect, giving you a small RAM boost. But don't expect stellar gaming performance. Good gaming today requires newer technology hardware (faster CPU, good graphics, and lots of RAM) and your motherboard and CPU are showing their age.
That said, with your starting point, you generally get more bang for your money by adding RAM before upgrading your graphics. With your small amount of RAM, most is being used just by the operating system, leaving little room for any of your applications. That means Windows and your CPU are constantly banging on the slow hard drive's Page File for extra "virtual memory" space. That's a huge (very skinny) bottle neck that will not change by adding a graphics card (the extra 8Mb is insignificant in that respect). With more RAM you will see dramatic improvements in over all computer performance. 1Gb is the "sweet spot" with XP and single core CPUs, but even 512Mb over your current amount will still yield significant results.
One other point - any new hardware will also place greater demands on your case cooling. It is essential to make sure you have good front to back air flow through the case and to keep the internals clean of heat trapping dust. I suspect this old computer uses wide, flat ribbon cables for the drives. You might consider replacing them with new round cables
as they have much less impact on that desired air flow. That case may only have one small case fan. I doubt it supports more, but while in there cleaning, check for more places to mount another fan, and an extra power connector.
Also, note this computer is about 10 years old. That's getting pretty long in the tooth for the electronics itself. While modest upgrades will extend its life a little longer, I would hesitate to invest too much in it. When (not if, but when) the motherboard fails, it will not be cost effective to repair or replace it, and a new, or at least newer computer will be necessary.