Get a used P4 system, will cost about what a RAM upgrade would be. At least in the US market. Whole P4 systems with 1 gig or 2 gig of RAM are abut $100 or less, much better use of money than upgrading a P3 system.
+1 to Area51's Crucial suggestion. That site can scan your system and tell you exactly what you have and what you can upgrade to. It's a rare Pentium III system that will go up to 1Gb by my memory - you may find each slot maxes out at 128Mb in which case a cheap Pentium IV would be the better option.
You don't have to buy from Crucial - just take the advice and run.