During the time of the Celeron 500, 64MB was quite standard. Doc is right though, you can pop up to 256MB of crucial for $50.
The audiophile itself doesn't have high requirements....it really depends on what you're going to do with it.
I've worked on 24 track 24bit/44khz projects with several effects on my old Celeron 500. It didn't run great, but it ran well enough to be usable (Windows 2000, 164MB RAM at the time). Of course every machine is different, and your mileage is sure to vary.
What do you want to do exactly?
Slackmaster 2000