Other answers makes a lot of sense to me, and I post this one just to expose an other possibility you may want to consider.
In my opinion (and experience), if you want to learn something, you may want not to try a single approach, but try to have the widest background as possible. @Argenti Apparatus' answer says:
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.
which is true. Yet, if you want to have as much experience as possible, you may want to work on older bikes as well as on newer ones.
The second point of learning whatever is that it is much more efficient (i.e. you learn more stuff for the same amount of time) if you are not alone. Again, Argenti Apparatus suggested watching videos, and I can't emphasize enough that this helps (in particular Park Tool's videos are great). However, what helps even more is to actually learn from other (more experienced) bike guys, to which you can ask questions, who can actually show you stuff on the actual bike your working on.
Finally, I'd emphasise that, sure, bikes improved over times and older components are different from the newer ones, but essentially, bikes are still the same than a century ago (imo, the last fundamental improvement is the derailleur): you'll have to learn how to adjust a bearing, how to true a wheel, how to adjust the saddle, etc. My point is that there is a lot of things that are in common to all bikes.
So, to summarize, in my opinion, what you may search first is: (i) people to help you; (ii) work on as much different bikes as possible; (iii) start working on what is universal on a bike, and specialize (toward newer/older/whatever kind you prefer) when you have this common background.
You may say: "sure, but where can I do that?". The good news is that there are a lot of community workshop all around the world. In those workshop, you'll meet a lot of benevolent people that are waiting to share their passion of building bikes, and most of the time, they are very good teachers, which will not only teach you the mechanics, but also the history of biking, the culture that goes with it, etc... Usually, they have a lot of bikes they can afford to lose in case you accidentally destroy some parts when working on the bike.
Also, having a dedicated (shared) workshop, with other people to share discussions, meals and drinks improves your motivation a lot!
You may want to peruse BikeCollectives.org if you are in the US, Heureux Cyclage if you are in (western) Europe, or otherwise discuss with a local bike shop, they may indicate you where the closest workshop is.
 One may say that it would be quicker to start working on your (future) bike directly, instead of studying different bikes before actually starting working on your bike. To that I answer that (i) in my experience, I have seen no evidence of being actually quicker (nor to be slower); (ii) if your goal is to learn, your main goal should be to learn and not to build a bike. Also, since this is a summer project for you, you have plenty of time (once you have a bit of experience, building your actual bike is a matter of days if not hours).
 To illustrate the quality of what you learn, let take an example. I don't know for other countries, but in France where I live, there is an "official" professional training (CNPC) to become a professional bike builder/maintainer. The fact is that what you learn in this training is (i) more to sell bikes than to repair/build one; (ii) the maintenance is pretty basic (you don't necessarily even learn how to patch a flat, since what professional do most of the time is to change the tube); (iii) you learn the most when you actually do your internship in an actual workshop.