What is it that you want to do with this old dell anyway? Sounds like it is already good enough to run XP. Is there a certain application you want it to perform better in?
If you really want to do some sort of upgrade on this rig, the biggest performance increase you can get would be to install a newer hard drive. The original drive in the Dell is likely around 20 to 30GB, and spins at 5400 rpm, with only a paltry 512kb or, at most, 1MB or cache. An upgrade a more modern 7200 rpm, 2MB or 8MB cache, 40-80GB hard drive would not only make your system much quicker, it would also make it a lot quieter. I recommend one of seatage's Baracuda IV or later hard drives for their reliability and excellent acoustics, but really even a Maxtor or Western Digital will do, the Seagates just happen to be single platter, producing less heat and consuming less power. More than 80GB could be problematic with that old Dell bios, so I would stick to 40-80 GB sizes to stay on the safe side.
If you want better gaming ability, you can go all the way up to a Radeon 9800 Pro, as many are dual keyed for 2x and 4x/8x. They cost around $50-$60 on ebay. This is the best card you could ever get for that system. A bit more practical though would be to pick up an old Geforce3 Ti200 off ebay. You shouldn't pay more than $15 for it, including shipping, which makes it a hell of a deal. It is a strong DirectX 8 gaming card, and should be low enough in power consumption to not put too much of a burden on your old PSU, which is one of the proprietary designed units (I have an XPS R450, which used the same case, psu, and mobo as your T600). With the radeon 9800 pro, you would have to install a stronger power supply, which would mean big bucks having to buy one of PC power and Cooling's Dell upgrade power supplies. Besides, between the two, your old PIII 600 would bottleneck both of them, meaning the 9800 is a waste of money over the Ti200.
If you want more CPU performance, you're at the point where it becomes cheaper to buy a slocket and install a Taulatin Celeron. No guarantee that it will work though. A Coppermine Celeron at 1000-1100 MHz would be a safer bet, and they're pretty cheap and should outperform the 600E with shear clock speed. A slocket and a Celeron will set you back around $25$30 for the two on ebay.
So, $25-$30 for cpu upgrade, $15 for Graphics Card, and $25-$55 for the Hard drive = $65 to $100 to completely upgrade your computer. Not terrible, but then again, that's a lot of money to sink into a machine only worth half that.