Bike building is a breeze. Sort of.
Generally speaking, all components are modular, inasmuch as they simply bolt on without needing to alter them or the thing you are bolting them onto. OK, you need to be certain they are all compatible with your frame and each other, but it takes some pretty rare combinations to mean they don't. As long as the BB standards are compatible with your crank, the wheel axles are the same width as the dropouts, the steerer is compatible with your headtube or you can get a headset to fit the two together, and your seatpost is the same as the seat tube, then go for it. Without boasting, a full build from scratch with compatible parts would be an enjoyable evening in the garage with a beer.
Go for it. You will learn a hell of a lot about your bike, your self and your abilities. It may take a few days, but Youtube is full of helpful "How To" guides. The previously mythical "indexing" of gears will evaporate into "what was so hard about that?" and as long as you are prepared to invest in a few essential tools, then you will provide yourself with a newfound sense of pride and ownership.