Board and revision number? BIOS? The CPU may not work out of the box with Coppermine. If you don't have another CPU with which to boot up your PC then you may be stuck with a non-functional CPU. Even if all it takes is a BIOS update, you can't do that if the Coppermine doesn't work.
Assuming you CAN run Coppermine: The Celeron 800 runs at 100 FSB, but it's way overpriced. I would go either with a Celeron 566 for US$60 and overclock it to 850, or just buy a PIII 700 for $150 minus whatever the price slash is going to be. (Final price <$100?) I can understand why people always recommend AMD Durons, but as far I'm concerned, it's not really a viable option because: 1) It breaks your budget (esp. if you include tax and shipping). 2) It requires a MAJOR rejigging of the computer. 3) It may require a reformat to get everything working correctly. However, this may be warranted if your motherboard doesn't support Coppermine properly.
My guess is a Celeron 850 = PIII 667 = Duron 700, give or take 50 MHz and depending on the benchmark/app. Note that the Celeron is overclocked and the PIII/Duron are at stock speed. Overclocking of the PIII 700 probably wouldn't be terribly hard, because of your VIA chipset. Your video will run at a reasonable speed, and you can slow your memory if necessary. But there is a strong chance you can even run that PIII 700 at 933 without too much effort, as long as you have good cooling. Guaranteed chips are also an option.
That Voodoo 3 will be fine.