Windows ME's minimum requirements is 32M RAM. I'm sure that machine's struggling because my grandparents machine with 64M doesn't do to hot!
Judgeing by the RAM and the OS, I'd say you got this machine around 1999 or so(or that's probably when it was made...) It should use either PC100 or PC133 RAM, which is still somewhat available. I suspect you only have one extra slot on your motherboard for more RAM, and that you'll be limited by 128M per slot. Most computers around that time could only have 384M max, and that was only if they had three memory slots(which yours might...) Two slots, obviously 256...
You could get more info without having to open it right off using CPU-z. Just run that and it should tell you what kind of RAM you're using and all. Just remember