And of course, the biggest upgrade you could make with gaming is, surprise, video card.
A GeForce 7800GT would be a good upgrade if you plan to use SLi eventually with it (SLi is two video cards connected together, but only available on certain motherboards).
I'd imagine your motherboard has PCI-express slots? If not, you need to upgrade. I'd recommend a Asus A8N-SLI or a Gigabyte board with PCI-e and SLi compatibility.
Pretty much. I'm not sure how the X1800 compares, but I've heard it said that the 7800 is better. I'm running an X800 XT right now, and I love it, but obviously you can do much better than that these days.
7800GT is the best performance/price.
The X1800 model that competes with it is a little slower on average. (not by much)
The X1800XT (512MB) though is the top dog for available cards for more money. It's better than the 7800GTX 256mb which is about the same price.
Nvidia does have one card out better (7800GTX 512MB) although it is basicly...not available just like ATI's last card (X800XT PE) was.