If you stick in another GB of RAM (under £25 at www.crucial.com/uk assuming you've got one spare DIMM slot), it should be fine for general use; I've run Win7 on a 2003 Latitude D600 (Pentium M 1300MHz) with 2GB and it was actually quicker than XP at starting applications and felt quite snappy in use. (I did it for a laugh when we retired a batch of them at work last year but ended up quite impressed!)
You won't get the fancy Aero desktop effects but apart from that it should be fine.
With only 1GB RAM, it should still be usable but you'd probably find it struggling once you have a couple of things open. I'd definitely avoid running any of the "mainstream" anti-virus/internet security suites (McAfee, Norton, AVG, MS Security Essentials) - they are all memory (and CPU) hogs. ESET would probably be fine, though - it's really light on resources. I've heard good things about Kaspersky too.
On the other hand, is there really any good reason to upgrade the system to Win7?