I have exactly the same "fantasy" as yours, I have tried many linux distribution but not yet including KNOPPIX(I have heard that the software installation is quite different from an origional Debian, that is, the HD-installed KNOPPIX is no longer a Debian), the following observations are based on non-LiveCD/DVD linux.
1. buy a NB or desktop which does not have a very "new" hardware, esp. graphics, network chip.
2. if you follow step.1, then maybe many Linux distributions can be installed successfully, if not, then the "Mandrake Linux 10.1 official" can be the first try, you may successfully reboot from USB HD "for the first time", but then you probably will get "kernel panic..." and can not boot any more. but somebody have succeeded that way, it really depends on the specific hardware(even the same NB model has different outcome !), but if you install from a desktop PC instead of a new NB, it mabye be easier.
3. if you find no luck in step 2. try install Mandrake Linux 9.2 then "upgrade" it to Mandrake Linux 10.1 official but does not configre the network, you will be able to boot from USB HD almost 100%, but if you configre the network, it will probably get "kernel panic..." and can not boot any more. again, if you install from a desktop PC instead of a new NB, it mabye be easier.
4. then you can manually configre the network, not the usual one from control center, which I have not succeeded...(maybe you can)
5. FC core 4 can not even showup its installation startup picture on my NB(Asus M6N)
6. KNOPPIX 4.0 DVD is the most powerful Linux I have ever seen, but socftware installation not "rpm" type, but debian type, which I am not familiar with, and have some dependency problems, some software just can find its .deb counterpart, and alien the rpm usually get lots of errors.
hope they help, if you find out some clean solution, I will be very looking forward to it.