There is the 810 chipset, and then there is the 810E chipset.
The 810 chipset can run FSB at 66 or 100, while memory always ran at 100. I'm not sure if this is a chipset or motherboard issue, but I don't think it can take Coppermine chips (FC-PGA).
The 810E chipset can run FSB at 66, 100 and 133, while memory always ran at 100. This can take any FC-PGA chip, so you can run up to a 1GHz P3 CPU (or 1.13, if those really are available), but why you'd want to cripple a nice P3 CPU with this chipset, I don't know.
My suggestion is to save up for more of an upgrade than an incremental CPU boost. What you'll want to save up for are all the parts that you can't take with you from your HP Brio system. Without looking at your system, here's a breakdown:
KEEP FROM OLD SYSTEM
PCI 32MB Savage4
128MB RAM
hard drive
CD-ROM/DVD/Burner (whatever you had)
PCI modem
BUY THESE ITEMS
ATX case & power supply
floppy drive (you can keep the one from the Brio, but it won't look nice)
motherboard with AGP slot and SDRAM support
CPU & fan/heatsink
Which you buy will depend on your budget and what tickles your fancy.