Do I have to take into consideration that anyone who hasn't heard anything before 1980 might well not like a good chunk of any of these suggestions, which I think are mostly good?
Due to the variety of styles I have to believe that the Beatles' White Album is probably the best choice. I'd give that the nod over the Stones' Exile On Main Street. What about some of the amazing box sets that chronicle the music of the past that have come out in recent years? There are plenty of R&B boxes, classic rock boxes, etc. I happen to prefer the label-based collections rather than the ones that chronicle individual bands or artists, and even more so in terms of answering a question like this.
As for jazz, I think that there is a spiritual element to Miles Davis' Kind Of Blue, which came a few years before the admittedly more concept-like A Love Supreme. Much as I love ALS, I have fairly idiosyncratic tastes when it comes to jazz & while KOB would certainly be the first jazz recommendation I'd make, I'm afraid I'd have to give Blue Train the nod over ALS. I think ALS is best heard after absorbing Giant Steps & especially My Favorite Things. I believe that adds a context that masks some of the odder moments that are to be heard in ALS. I don't mind the moments I'm characterizing as odd, and they're not necessarily 'odd' to me personally, but I use that word because even to jazz fans who are big fans of most of the more common forms explored prior to the most-serious experimentation of the 1960s, there are moments that are counter in one way or another to the perceptions of many with regard to jazz music in general on that record.
As for Frank Sinatra, I'd say Songs for Swingin' Lovers. Like my other choices, I know it's obvious. But sometimes obvious choices make sense, and are choices that are made for a reason. I think this is one of those records.
But all this aside, I might just have to cast a vote for Iggy & The Stooges' Raw Power. For some reason, given the question, I'd put that record before any by my punk rock heroes of the 70s (& prior), and it might just be a strong #2 to my initial recommendation of the White Album, which I feel has to stand. And then there's Quadrophenia. And then there's the early Led Zep albums. And then there's the Beach Boys (Smile, a well-constructed boot version, that is, over Pet Sounds). And then there's the Velvet Underground. And then there's Elvis Presley. And Elvis Costello. And James Brown. And Wynonie Harris. And Louis Prima. And Tom Waits. And Howlin' Wolf. And Big Joe Turner. And Chet Baker. And the Ramones. And Big Star. And Ray Charles. And Dylan, of course. And Roxy Music. And Ellington. And Armstrong. And Bille Holiday. And and and.....