In my case Revolver is both (probably) their best and means the most to me. I recall it clearly under the Xmas tree when my older brother got it. It was flipped over so the lads, smiling in their trendy sunglasses, was the first I saw of it. It was a few years after it came out. I was probably 6 or 7. Hard to recall. But it's one reason I associate the Beatles with Xmas. Can't beat two good things being so closely linked.
The cover that means the most to me though is, curiously, an album neither my older brothers nor I owned until I got it on CD. The shadow shot on With the Beatles is one of the earliest images I recall of the Beatles when I was very young. But it was on a single, I think All My Loving, that I first saw it. I think it had a pinkish trim. Regardless it was a haunting image for a lad who was still a toddler.