No Crashes - What Specs?

Now that I've made the move from dial-up to high speed (DSL) I'm ready
to ditch my five year old Compaq very soon.

The main problem I have with this computer is that it has always crashed
a lot and seems to crash more and more.

It's running Windows ME, 850MHz Pentium III, 128MB ram.

Now that I'm on a modern high speed connection I want a computer that I
can keep on for weeks at a time. I want a computer that will not crash when
I'm listening to steaming audio while surfing three or four different web
pages at the same time, while downloading content.

What do I need in a computer to accomplish this? Is the solution to
just move up to Windows XP? How much ram do I need? Is 500MB enough for my
needs or should I move up to 1GB?

I don't play games on my computer (I have an XBox for that) except for
online chess, poker, and backgammon. So, I don't need a maxed out system.

I do play a lot of music on my computer and store a lot of pictures from
my digi-cam.

So, what would the minimum requirements be for a computer?

The most important thing I want is a stable system.

Thanks