If your thinking of upgrading because your computer is slow, you should first checkout how to fix your slow computer first.
Below is some recommendations about upgrading different parts of your machine.
More memory (RAM)..
The biggest cause of any old computer being slow is lack of memory.
Most computers will make use of all the available memory it has, and if it does not have enough, it will start to use the harddrive as memory. (called 'virtual' memory, stored using a 'swap file'). This slows the computer right down. If you have a lot of software on your machine, or play some of the latest games then you need a decent amount of memory. If you find your computer constantly accessing the drive when clicking on different windows or closing windows then its likely you need more RAM. As a rule of thumb I generally recommending around 2gb, anything less than 512mb is just not enough.
Get an additional hard-drive and move your video files and mp3 music off your old drive on to the new one. This will help free up your primary disk so that your system can run faster. Also keeps your files safe in the event of a complete system crash.
New Graphics processor..
If you play a lot of 3D games then you need a decent graphics card. Before upgrading, do check that you do need a new card. Check you are running the correct graphics drivers for your current graphics card. The wrong driver can sometimes work, but the graphics performance will be poor. Also check you have the latest 'directx' software. This is available free from the microsoft website.
If, after doing the above you think you still need a new card, then the next step to figure out which cards your computer supports, as some cards will not fit. Generally there are two types, PCI and AGP.
Personally, I would look to buy a completely new base unit (motherboard, cpu, harddrive, graphics, sound) instead of upgrading the bits inside. You can then pull out the harddrive from the old machine and add it to the new system as a secondary drive, so that you can still easily get to all your old files.
There are various types of processors, only curtain types will fit in to your machine. If you not completely sure about what your doing, then I again I would recommend buying a new base unit instead.