I had read the "paper" version of the Right Stuff many years ago. I can remember the Apollo missions from when I was young, though I thought of it as "normal", not a big deal (they seemed to be going to the moon all the time, and taking over my regular TV shows).
I didn't remember much about the X-jets (X-15 to 20) that were running in parallel to the Mercury missions, and did some rather breathtaking things (like going 70 miles up in the air, 20 miles into "space"). My big takeaway is that planes don't work well with little or no atmosphere, and pilots can find themselves in spins that the planes cannot break out of (e.g. flat spins or end-over-end). If they can manage to get the spin onto an axis that allows the flight controls to operate, they can then recover. Chuck Yeager's abandon ship flight is well-told of the events.
As with Gene Krantz's book "Failure is Not an Option" about the Apollo missions which followed (Mercury - one astronaut flights - "the Right Stuff", Gemini - 2 person, Apollo - 3 person - "Failure is Not an Option), I'm amazed at the number of problems and "near misses" that occurred - Scott Carpenter running out of fuel, John Glenn dealing with a concern that the heat shield might not be securely attached to the returning capsule.
The "stuff" of the Right Stuff is interesting as well - test pilots (any advanced pilot) must convince themselves that they are the best there is, in order to handle emergencies and deal with the relatively high odds of crashes and death. The odd side of it is that when there is a crash, even if no objective observer can find fault with the pilot (e.g. wing fell off), still, the "Right Stuff" demands that there be a difference between the "failed" pilot and the "still living" pilot - something like "How could he have flown without checking that the wing supports were intact?". This philosophy may help to handle the stresses of test pilot life, but it is certainly somewhat fictional - complex aircraft are a team effort (ground crew, engineers, pilots) and it would be impossible to check every aspect on each flight. It seems somewhat sad to me that each pilot who died was somehow denigrated post-partum, as part of the illusion-maintenance of "the Right Stuff".
The Mercury project was a departure from "normal" test pilot "Right Stuff" as the early flights (and really, most spaceflights) were virtually all automatic and computer controlled. It was only the insistence of the newly heroic astronauts that enabled them to have some control over certain aspects of the flight - which did come in handy on some flights. It took a while for the "monkeys did the job first" to give way to the massive public adoration of the astronauts in order to have the "astronaut" path be considered an apex for flyers.