an old system like that would work but from experience of having a slow laptop (300mhz), it just is nowhere near as good as current ones. I guess since the P3 was around 1ghz, it would be significantly faster than the one i had, and much more useable. one thing that will be somewhat of an issue is the screen size andor resolution. i'm not sure what the ones you're looking at have, but i'm guessing it's either svga (800x600) or xga (1024x768), and both of those (especially svga) are not good enough nowadays.
well, if you're really planning on just doiong the very basics, the p3 generation should be fine at like 500MHz-1.2GHz. i mean, if you think about it, half the time pentium M's run at 600-800mhz on speedstep. it also seems that most of the screens are xga (i saw a $350 latitude with a 15" uxga)
two things i'd recommend making sure of. first, make sure you get a decent screen. if you're browsing through forums or ebay or wherever, having lower resolution is going to slow you down. second, consider that most of these laptops are pretty old and are used systems. they will thus have seen more wear and tear than a new laptop. two things will possibly be problematic: the hard drive and the battery. the battery after lots of usage will most likely not hold its full charge as it is most likely not a new one, and a new battery could cost a decent amount. the hard drive, being from the P3 era (what, like 4 or 5 years ago?) will have been used to a good extent probably, and will be more prone to failure and will probably be louder than a new system.
consider searching around ebay for the low end pentium M (not the pentium 4 M) systems. they will more likely be significantly better for just a bit more. or yeah, what qhn said about amd systems. they will be better than the P3. also, i would recommend at least 512mb of ram.