First you have to know if your motherboard supports a 133MHz fsb processor. The Pentium III FCPGA Coppermine comes in both a 100MHz (very rare) or the more common 133MHz fsb version.
If you do not have a cpu purchased already, forget the 1GHz PIII. Get a socket T converter and pruchase a 1200-1400MHz Celeron Tualatin and save a bunch of money. It will still have 256k of L2 cache and with data prefetch will be faster clock for clock than a Coppermine (of course 1000MHz is the fastest Coppermine P3).
If your motherboard and ram support a 133MHz fsb you could actually get a 1GHz or 1.1GHz and use a 133MHz fsb to overclock it to 1333-1466MHz.