98 and later were much better at plug and pray than 95 was.
But either way, I got better results by copying the cabs (winxx) directory to the blank bootable hard drive (boots to c: prompt) and running setup from there.
I had done what you described (take an already installed OS on a HD). I allowed the boot up to install everything new it found, and I removed everything unused. It worked fine. But it took as long as a later clean install did, due to the multiple reboots before all the new drivers were happy.