There are many reviews showing the difference between the P2, P2-C, and P3. Spend 5 minutes surfing and you shouldn't have any trouble finding a good review.
Quick answer: Clock for clock, the Celeron is as fast as a true P2 in most situations (particularly games). Only downside is the slow 66mhz bus speed which can hurt performance. Get a 366 or 300A gauranteed at 550 or 450 (respectively) so you can get the 100mhz bus speed and you've got a P2-eater machine.
The P3's SSE optimizations are now starting to become important. Clock for clock, the P3 is pushing past the P2 architecture in a games (especially with G400 cards). You can get P3-450s for about $175 now, though. It seems like people are having great luck overclocking them to 550-600mhz (in fact, it seems like almost all post Celeron 433, and P3 chips reach 525-600mhz). Only downside is you end up with a 124-140mhz bus speed which some devices don't like. NICs, modems, and old ISA soundcards might screech at running a 24-40% higher bus speed.
My advice: If you have the cash, spring for the P3-450. Maybe overclock it a bit if you dare. If not, get a gauranteed Celeron 366/550 off ebay, or if you don't like overclocking get a Celeron 466.