Yes, the P3B-F will support
any speed processor (with the probable exception of the upcoming Tualatin), so long as you have the latest BIOS update. All revisions of the P3B-F do not have voltage problems related to older revisions of the P2B. The P2B family of boards were completely different anyway.
The latest BIOSes are
Version 1006 Final and
1008 Beta 002. I'd go with 1008 Beta 002 as it has full support for the latest cC0 and cD0 stepping CPUs.
The 1GHz Pentium III is available as both a 100MHz FSB part and a 133MHz FSB part.
If you decide to purchase the 133MHz FSB version, due to the lack of 1/2 AGP divider on the BX chipset, you will be running the AGP slot out of spec at 89MHz. PCI will run at 33MHz, so nothing to worry about there.