Will a sata or sata II drive work on my pentium III computer :
no you need a motherboard that supports sata /sata II (at least some pentium 4 board would support)
From what i see, change the whole computer: it's a dinosaur.
even if you change the cpu to a pentium III 1 ghz + 512 mg memory it would still be slow
If you have a tight budget buy a pentium 4 3.0 ghz + 1 go memory + wd 500 go (32 meg) if you want to see any improvement (you should pay around 150 $ )
event then it would still be slow.