Learning how to build a bike: Is it better to buy a used bike and disassemble it?
Messing with a used bike will teach you a lot (mostly through mistakes, but that's how the process works). There definitely is a huge advantage of having hands on experience figuring out how to adjust brakes, derailleurs etc.
The disadvantage of working on an old, cheap bike is that the components will be old designs and standards which does not give you experience with more modern stuff. I think if you combine working on an old bike with watching YouTube videos and reading articles you'll learn about newer standards as well.
The trouble with buying individual components is you have to know what you are doing to make sure you order parts that are compatible with each other, and you can make expensive mistakes. Also, constructing a bike from components is quite expensive relative to buying a pre-built bike.
One thing to consider, if you have a bike for wrenching and learning on, expect it to be out of service some of the time, so you'll have to fall back to rental bikes at times.
Online bike wrenching resources to get you started:
Sheldon Brown Classic source of bike component information, covers older standards comprehensively.
Park Tool Repair Help Very professional, clear and comprehensive guides to [dis]assembly and adjustment
RJ The Bike Guy Just a guy wrenching is his garage, but he knows what he's doing and he tends to get into older bikes and components.
Shimano Product Information Shimano provides extensive and detailed info and specs about their products (including older products going back to 2004). This will look very daunting and first but will begin to make sense as you learn.
And of course https://bicycles.stackexchange.com/ :-)