I got into a lot of 60s music from the oldies station as a kid. "Eleanor Rigby" and "Get Off of My Cloud" were two favorites. And "Liar, Liar" by The Castaways.
I got into The Beatles' records before my teens, especially Rubber Soul and Pepper. Then lots of others: The Stones, Kinks, Zombies, Beach Boys, Zappa, Doors, Bacharach, Stooges, Velvet Underground, Love, etc. I'm probably forgetting a bunch. The first things I bought when I had a job at 15 were The Complete Robert Johnson and Nuggets, which had just been rereleased as a box set.
I love the old Corman movies from that time; The Monkees' Head; Batman: the Movie; Psycho; Alphaville; Planet of the Apes; Easy Rider; and more.
There was a great sense of design in the art and animation. The illustration art in ads, too. Lots of beautiful stuff, which was creative, and not sleek and business-like.
There's a lot of great jazz from that time, too. Miles Davis' albums were explosive, brilliant, and new, even if rock was more of a cultural focus.
I love Nuggets and Dominic Priore's old Beach Boys scrap book as time capsules of that period. They're just a small part of it, though. However, when we talk about the 60s, it seems we really mean 66-69. Maybe 64-69, as Beatlemania was a sea change.