Actually, there are Slot 1 PIII's with the cache on die, as well. The IMPORTANT part is not whether or not it is FC-PGA or Slot 1, but whether it is the older Katmai core or the new Coppermine. The Coppermines have the fast on-die cache, the Katmais don't. Coppermines can overclock, Katmai's generally can't. Now then, Coppermines are availiable in both FC-PGA and Slot 1 forms, and the Katmai's are only Slot 1. How to know which is which? The Katmai's have 512KB of cache, the Coppermines have 256KB. You won't likely be able to run a 800/100 chip on a 133 side bus, it won't overclock that high. Better to get a 700/100 if you want to do that, they hit 933/133 fairly reliably. But if you're set on a 800, get the 800/133, it will be much faster than a 800/100.
Can you use the old memory? Yes, if you buy a motherboard with the 815 chipset. That would allow you to clock the memory down, but remember, when you clock it down like that, you lose the benifit of having the 133 bus in the first place.
My personal advice would be to get a 800/133, don't try to overclock it and don't worry about whether or not it's FCPGA. If you want to overclock, get a 700/100 FCPGA because it will make the jump to 133 and there are lots of Coppermine ready FCPGA heatsinks out there that can help you get there.
FCPGA on an adapter is worse than the other two, as long as you have a motherboard that lets you do the overclocking on it. If you have a dumb motherboard, you'll need the adapter to change the voltage and stuff.