Heya.. I'm in the process of doing almost the exact same thing with a Dell Precision 410...
First thing, as poof said, is to get a bios update- goto support.dell.com, enter your service tag or system model and goto the downloads section and grab the most recent flash bios update (these usually come as annoying executable which wants to unpack itself onto a floppy). Read through the release.txt file and see if it says anything about PIII's. Mine has stuff like "Support newer steppings of Pentium III Processors." dated 2/16/00. Hopefully you've got something similar. If so run the bios update and then try and figure out which PIII to get.
The early PIIIs that poof suggested are the most compatible as they run with the same voltage as PIIs. These PIIIs all have the larger (and slower) 512k cache and come in speeds from 450 to 600 MHz.
The newer coppermine PIIIs run at a lower voltage which your motherboard may or may not be able to supply. If you can locate any documentation that states that your motherboard can supply 1.65v then you can get one of these in the 'slot1' cartridge. These CPUs come with 256k full speed cache in speeds 600MHz+ in 50MHz increments, look for the 100MHz FSB (front side bus) versions as there are 133Mhz FSB ones (I'm not sure how different the 2 versions are)...
Myself, I was was not able to find much documentation on my motherboard, but I have a good feeling that my old system cannot do 1.65v. I'm gonna try to get a 'socket 370' PIII 750 and a socket 370 to slot1 converter which has some voltage control on it (the 'slocket' that poof mentioned). I'll be ordering them in about a week (after payday- yay!) so if you want you can wait to see if I have any success with this...
Good luck!
bliab