I'm a full fledged computer geek, so I guess I'm qualified to offer some suggestions. I agree with Mid Life Crisis that an upgrade is in order if you're still running Win95. Windows 98 SE (Second Edition) has been very stable, and has all the drivers you should need for whatever you have connected to your computer. I too have an Aptiva, and 98 has been great.
I never saw anything special in Windows ME to make me recommend it. I've been testing the new Windows XP which is due to release later this month, and it is incredibly stable and even seems to run a bit faster. If you wait a few weeks you could buy it, but I'll warn you that since it's so new (and not actually released yet) I have several things I can't find drivers for. If any of your equipment is more than a year old, I would recommend waiting before you move up to WinXP.
With all that said, there are some things you can check that may help your system now. Some things I've seen help stabilize the system include:
Closing things on the task bar. If when you turn on your computer, a lot of things load in the task bar automatically, look at removing some of the unnecessary ones.
Reduce the number of colors being displayed. You'll actually see little difference if any between using 16 thousand colors (16 bit) and higher settings. This will free up video memory, and tend to stabilize things. Fewer colors than that will look crappy.
And finally, check the windows update site for the latest patches and newer version of Explorer (assuming that's what you're using for browsing).
Hope this helps.