Well you could do both, buy a used bike and then slow-build it.
I built mine with new parts from Nashbar, Amazon and other online sources and it did cost about what a new bike would. But I wanted to use all new parts because I needed to know that if a problem arose it was something I probably did and not a worn-out part. Over time I've swapped out wheels and drive train parts, everything except the frame headset and fork in fact. Sure, it's a good way to spread out the expense. If you like to scrounge for used parts you could come out way ahead, buy new parts and you won't.
As far as I'm concerned, if you don't go off the deep end buying a high end drivetrain, or stick to 8 or 9 speed, most of those parts are practically consumables.