My approach with bikes (as with most other things e.g. home DIY) has just been to acquire the skills when I needed to.
I have known how to remove wheels/fix punctures since I was a kid when my brother showed me how.
Here's a few examples:
Example 1
About 10 years ago I was going to throw away my commuter bike because the freewheel teeth were worn so badly the chain was just slipping all the time. I remember visiting
Halfords, where the mechanic advised me that there were about 17 different sprocket removal tools; while neglecting to mention that by far the most common, at the time, was the Shimano one. In my opinion he was just trying to put me off. I eventually found the correct tool online and successfully used it to remove the freewheel and fit a new one. This also started an interest in using cheater/breaker bars as it was a ****** to remove.
Example 2
I bought a new roadbike in
Decathlon - BTwin Triban 3 - and discovered that the bike technology was new - bear in mind that the kind of bikes I ride are well behind the curve (trailing edge technology). It had a cassette and a freehub which was new to me. So the first time I cleaned the drive train, about 6 months later I bought a cassette removal tool. For the chain whip I used a car filter removal tool which was similar.
I now have a proper chain whip which came with a box of tools I got as a Christmas present.
Example 3
I had a series of broken spokes on a bike I used for commuting; Each time it happened, I replaced the spoke with a spoke key and just tightened it, until the tension was roughly similar to the other spokes and the wheel was roughly true. This led to an interest in wheel truing. I remember finding a video where somebody (I think it was C J Hoyle [see YouTube]) explained how to true a wheel using the brake blocks as a makeshift truing stand. My daughter then bought me a truing stand that Christmas (It was a nice surprise!).
Through all these little learning experiences I have gradually built up a nice little toolkit. A part here, another there. Improvised tools from Sheldon Brown; all sorts really. I keep them all in a metal tool box just for bike parts.
I find curiosity does the rest.
