The BH6 is a nice board with one of the best chipsets ever - why replace it when you just need a CPU? Just get an Intel Pentium III Coppermine of the cB0 stepping and preferably in the FC-PGA format (you'll need an inexpensive 'slocket' adapter to match it to your BH6 too). Spend as much as your budget allows, upgrade the board's BIOS if you need to, then put that new baby in your board and overclock it as high as you can. Down the road you can get a new mobo based on the new Intel 815E chipset and the FC-PGA P3 will plug right in.
And you won't have to look back. The Coppermines are excellent overclockers and stock are faster than the Celerons, Durons, and old Athlons. The new Athlons/Thunderbirds are only marginally better than the Coppermines and the difference is not worth switching platforms for.
Finally, I think you'll notice that many of the newer motherboards are getting more expensive than previously , especially for the AMD CPU's (I saw an A7V for Duron/Tbird @ $210 shipped). I think the days of cheap VIA-based mobos are coming to an end.