BoR65,
WinXP will likely solve most of your problem. The issue lies in that WinME manages memory poorly. Regardless of how much RAM you have, your "resources" will still drop at the same rate, since that term refers to your System and GDI heaps, not your RAM (per se).
The quickest and easiest way to solve this problem is to limit the number of extraneous (and often useless) programs that start up as Windows starts and then run in the background, doing essentially nothing.
Yo can see what you have running at startup by default by going to "Run" in the Start Menu and typing "msconfig". Look in the "Startup" tab, and disable any apps that are set to run at startup that you don't need. Be careful, though; some of those apps (namely "Explorer" and "Systray", unless you're running Litestep or another alternate shell) have to be running, as well as proprietary keyboard and motherboard softwares that your PC manufacturer may have set to run.
Luckily, WinXP doesn't handle memory in the same fashion, so the problem is more or less moot in it.
Hope this helps.