...what is the latest version of Windows that will run well (not just run) on a 450Mhz PII, and how much disk space will I have to waste on it?
Running "well" is totally subjective
I think WIN98SE would run well. I have run WIN2K on a 300MHz PII and I thought it was quite slow. I have no experience with WIN ME.
Depending on what you're using the computer for, I would think that 5 gigs is plenty for WIN98SE, and 20 gigs is plenty for WIN2K... but if you're storing videos, high-rez pics, tons of MP3s, etc, then you'd need larger drives regardless of operating system.
As jdhurst points out, a faster processor will let you run a later OS. There are many Slot 1 PIIIs out there that people are practically giving away. You can also find adapters that will let you run even faster Socket 370 PIIIs, but these may be a little pricey.