The Right Stuff, now -- with the 50th anniversary of Apollo 11 -- would be the perfect time to do it. There is one caveat based on what we have learned since the book was written: the author was too tough on the late Gus Grissom. The Kansas Cosmosphere raised Grissom's sunken capsule and they learned that Grissom's account of the hatch "just blowing" was true. Regardless, the book is terrific.
And, my all-time favorite compliment about my book, Warnings, was when it was favorably compared to The Right Stuff by critic Tom Fuller. So, read TRS and then read Warnings and you'll end your summer with two great books!