Basically, you could go for a 1.3GHz Celeron as far as cheap CPU's go. The motherboard likely supports the Tualtin Pentium III's that scale to 1.4GHz. However, if you're going to build a new system, I wouldn't say replace everything, but any video card you use will be hampered by the PCI bus. I would not invest anymore in that system and just save up for a new rig.
Reasons why:
1.)You've got a micro ATX motherboard. While these aren't uncommon, if you stick with that case, you'll have to stick with a micro ATX motherboard.
2.)Power supply. If you stick with a mATX board and go to something like a high-end P4 or Athlon along with a nice graphics card, that PSU may not be enough. You need at the bare minimum a 300W PSU conforming to the ATX 2.03 spec, which requires an additional 4-pin, 12V auxillary power connector implemented when the P4's hit to supply extra juice for stability. My guess is that the current PSU is probably a 250W max and isn't to the current standard. That's not saying it's bad, but it's most likely not going to be enough.
3.)The 1.4GHz Pentium III runs around $140 new. Your system wasn't intended to be a real power rig, and with the lack of AGP, you're very likely not to notice an improvement particularly in gaming.
4.)RAM. DDR SDRAM is the new standard and is also a better value. SDR SDRAM like you use, is being asked for less, and the price, you've probably noticed, is already going up in price.
You can pick up a basic ATX case for around $50 at local shops. You can buy them cheaper online, but I don't because of the high shipping costs. That and a new PSU (choose a brand like Sparkle or Antec) of at least 350W would be the first step to do if I were you.
The next step basically has to be done together.
New motherboard, CPU, and RAM---at least 256MB. Before you do this step, backup your system, because you'll want to reinstall windows. Any modern board uses DDR, and right now you're looking at PC2700 (333MHz) or PC3200 (400MHz). The restore disc may or may not work for the new system.
After this, go ahead and look at an AGP video card, more RAM, etc. You can reuse the drives, so if the current space is working for you, don't worry about it. If it is, wait until you do the first 2 steps, then go for it.
What they mean by a PCI AGP card is simply a graphics processor that typically uses an AGP bus has been adapted for use in a PCI slot. Since the graphics card tends to be a bandwith hog, the limited bandwith on the PCI bus that's already serving other devices in the computer, is having to share with the graphics card.