If your board supports it, I'd go to an Athalon XP. The price difference between a Duron 1200 and XP 1600 is negligable. $35 in Canada. So, like 22$ in the US.
If your board doesn't support XP, the Duron 1200 will be a good stop-gap until you gan get a DDR rig. Realistically, it's your only upgrade path. Anything else will require a motherboard swap, in which case you will need new RAM and might as well get a better CPU too.
I think that a 1200Mhz box will be "good enough" for a little while more. One of my friends run a 800Mhz whith no complaints. He can play Diablo II, Quake III, Soldier of Fortune II without problems. He, of course, wants to put in an XP 1800 though. I have a 900 Duron that is still doing well, but I dont game heavily.
Your video card is likely going to become your new bottle-neck after you upgrade...
What are the requirements for Doom III? I think that will dictate what you need to do.