Since your current pc is that old it won´t be possible to upgrade it in single parts.
If you want a new CPU or a new graphics card you will need a new motherboard (different socket and PCI-Express connector). Therefore you will need new RAM and probably a new PSU as well.
So you are left with the drives and the case from the old PC. But you should also change the hard disks because otherwise they´ll be a big bottleneck in the new computer.
Basically that means that you need a complete new PC, if you want to do any upgrade.
For a gaming PC the most important part is the graphics card. But if you decide to build one try to match the components so you don´t have bottlenecks.