To be honest, Windows ME is such a basket case that I'd stick with Win98 and take the risks. With a decent firewall, and care over viruses, it will provide good service.
Or get really "different" and try Linux!
I converted my previous PC from Win98 to WinME, and needed very slightly more HD space. I converted it back to Win98 not long after that, because it was too unstable to use.
I later ran it dual-boot with Win2000, which was excellent, stable, etc but didn't have the drivers I needed for the peripherals. So I used W2k for "real" work and W98 for other stuff. That PC is now up in the Welsh hideaway and working fine, using W98.
Does the laptop have the capability of fitting a larger hard drive? That would be a good fix!