There's callbacks all the time, the entirety of the Master's History is an arc, likewise with The Timelords, and the Time War with The Daleks, Rassilon....Eh, how do you explain The Master, who has a much, much longer Arc? Or Time Lords and Gallifrey? Or the Evolution of the Daleks. There's a rich history throughout, that could be summed up in a sentence or two, or could be discussed for an hourThe Key To Time was a good storyline but then nobody liked the idea of a season long stor arc at least they had the benefit of two those stories being written by Robert Holmes. But on the new show River's story arc was stretched out over four years, she'd be a hard character for a newbie to understand at least to me.
Outside of the Master trilogy I'd hardly call any of those storyarcs. But with River it was known that she'd gone to prison for murder and it wasn't til the end of the last season that we learned the how and why. But with River since we didn't know much about her ourselves she was hard to understand while they were filling out her storyline to try and explain it to somebody else.
My first Classic Who story was Tom Baker Robot, where he's Regenerating, then the next one was Logopolis, where he's Regenerating again, something with this much history, if you jump in, in the middle, you won't get every joke, but, you can ride along following it as best you can, and eventually become acclimated