You've actually already got a fairly good understanding of your own issue and it really has less to do with any particular program than operating system versions and hardware limitations. Regardless of what you do, a Win9x based OS will run out of resources often far before it really runs out of RAM, simply due to that outmoded memory model. And any processor less than 1GHz will sruggle to deal with any current application of more than insignificant purspose, let alone a security scanning application which are generally quite proccessor, disk and even RAM intensive.
I've got an old PII 400MHz, 768MB, 20GB PC with Windows 2000, and though it has enough capacity it's quite slow to startup and TeaTimer simply adds to that issue. Though it has improved some due to recent TeaTimer rework, it's basically just processor starved on this system and so I simply don't try to do anything until it's had several minutes before login and then again after login while TeaTimer starts. Fortunately, I only really use that system for testing, so it's not an issue to have to wait.
It's relatively pointless to attempt to specify exact specs for any software today, since there are simply too many variables including not only hardware and OS, but especially the other applications already involved in startup on a particular PC. Sandra has already given you an idea of the typical RAM utilization of TeaTimer, but processor is much less easily defined, since it depends on so much else. I threw out the 1GHz myself simply because that generally implies a PC produced around 2001, when Windows XP was just about to release and 256MB of base memory was already considered normal, except maybe for laptops.
Since Windows 7 will be released later this year in many cases purchased with a new PC, I'd try to get your non-profit connected to some businesses that either refurb or directly donate used hardware in hopes of getting at least reasonable Windows XP based hardware. Anything else is simply a huge waste of your own time since it's unsupportable and only good for toys for the boys as you've mentioned, beyond being a huge security risk if placed on the Internet. There's likely to be a fairly large PC replacement trend as we begin to come out of the recession and those with the means take advantage of the relative bargains that are or will be available.
My own W2K system mentioned above will be relegated to back room status at best by next year since Microsoft will be ending Extended Support (no more Critical [Security] Updates) for that on 7/13/2010.
Bitman
