You have to get an FC-PGA slotket adapter in order to use the recent(or not so recent) Coppermine128 Celerons of P3 Coppermines, which I'd recommend. I have a Celeron 566 on mine clocked to 850MHz, but you could probably do better if you want to overclock.
If you wanna overclock, get a Celeron 666/700/733/766 and clock the FSB to 100MHz. With good cooling, at least the first 2 should work. I wouldn't recommend overclocking P3s because that would put the FSB too high(133MHz perhaps) and the BH6 doesn't support high AGP/PCI dividers, so this would also overclock the AGP and PCI bus too high for comfort.
If you don't wanna overclock, then grab the fastest P3 Coppermine you can get, which is probably a 1.1GHz one. Don't worry, the Abit BH6 will support it. Just grab the latest BIOS.
I wouldn't recommend the Duron+new mobo option if you're on a budget coz it wouldn't seriously outperform a 1.1GHz P3 Coppermine, and would cost too much, since you'd probably have to get new memory(DDR-SDRAM) as well.
A 1+GHz Celeron/P3 could still last you at least another 1.5 years if you have a good graphics card and you're not doing anything really intensive.