You probably won't be able to use your old memory, unless it's PC100 or PC133. PIII-500 is 100MHz bus speed with 5X multiplier. PIII-500 is Slot 1 configuration.
PC100-133 memory is expensive because it's no longer manufactured but still available. PC133-128MB is $50.
I just finished my upgrade. Found a computer in the trash, PIII-667EB. CPU was good, but mobo BIOS was trashed, unable to flash it. Power supply was blown out, which probably killed the BIOS/CMOS. Put CPU in place of my PIII-450. My BIOS/mobo allows manual settings of multiplier and FSB. Had to underclock because one memory stick is PC125 (that's right...PC125) and it's rated at PC100. It's Micron and not some no-name brand. Set multiplier to 5X and FSB to 112, so CPU runs at 560MHz.