An old Fuji with an 8 sp hub sounds pretty good to me. I have an old Trek I did that to, and it's excellent. The bike you're thinking of building is probably better than what you'd buy for similar money, so I'd say go ahead and build it.

Bear in mind, if you build up a custom bike, you will be more or less stuck with it. It's much easier to resell a bike in original condition than a rebuilt one, especially if its repainted as well. So if you're quite confident the rebuilt one is what you want, then no problem; if you're uncertain, be sure to save all the parts so you can put it back together if necessary, and don't paint it.