I ran Win XP with 128 MB of memory at work for 2 years (P3 800 MHz). It runs just fine. I've used Word (with 300 page dissertation open), Excel (with multiple large files open), Powerpoint (with medium sized presentation open), MathCad, Visual Basic, McAffee, and Zone Alarm all running at the same time. Sure there may be a 1-2 second lag switching programs, but it runs ok.
Recently I got a free boost to 384 MB on that computer and I cannot see much difference at all.
Your situation seems similar to mine. It'll work no problem with 256 MB. Yes you'll have the occasional swap of memory with the HD, but with just Office work and Internet, it will be minimal. More memory will buy you very little difference.
Just be sure to turn off much of the eye candy in Windows XP. Biggest memory eater of course is the fast user switching. But even things like a fancy background and screen saver can eat up 1% of your 256 MB memory - so just use simple ones or none at all.
Use the computer for a day, then go to the task manager and look at the peak commit charge. If it isn't much above 300 MB, you'll see little if any benefit of more memory. (A slight swap to the HD of some memory is typically done with Win XP regardless of how much memory you have, thus I didn't say 256 MB in this paragraph).