Flagrantly borrowing an idea from A Journal of Impossible Things, let's poke around some of the classic adventure formats and see what makes them tick. If I go on long enough, we can build a whole thirteen-episode series of adventure ideas. Remind me to include some two-parters.
This run originally started with the Historical, but the Season Opener leapfrogs it because it has to really.
1: Hello, Faithful Viewer!
The Season Opener (and indeed Series Opener) is the jumping-on point for new audiences, characters and players. It might be the actual first adventure in a run, or it might be a later jumping-on point when you gain a bunch of new players, but either way it's an introduction, setting up the format of the show.
In the new series this is generally a fairly normal modern-day adventure with a new possible Companion meeting a Mysterious Man who's taken an interest in the strange goings-on in her area, and proves smart and determined enough to keep up as he runs through it, helping to save him and/or the world into the bargain.
So it could be a spotlight episode for a new character, establishing why they're worth having at the gaming table. But this might be a bit too much spotlight for a new player, so they have to be woven in a bit more discreetly if they aren't as confident. Set the action around their lives, give them chances to step up, but don't push them front and centre.
Of course, it could also be the introduction for everybody, so the spotlight has to move around. Generally the more confident players need less to work with here - ideally, a confident player with a Time Lord can come in and be mysterious and dashing while everyone else is reacting heroically but normally.
And it doesn't have to be like this at all - it just has to be a reason for the PCs all to end up together and hopefully willing to work together and have adventures. It could have one whole scene in their normal lives and then transport them to any kind of adventure through a wibbly-wobbly time effect that the time travelling PC comes to investigate, for example. But hooking the audience with a classic Whovian mix of the mundane and the fantastic is a good place to start anyway.
It can also be used to plant any plot arc you want to have going through the run.
Example: The Last Day
History student Emily Stevens has always been curious about where ghost stories and other legends come from. So when she hears about a local myth about a cloaked figure riding through the campus quad at midnight on a given night, she has to stay up and take a look... and is surprised to find a Mysterious Man also taking an interest, waving a pen torch around like a Geiger counter and muttering something about "the last day." And she's even more surprised when the Dark Rider appears out of thin air and tries the run the man down as he confronts him!
The Dark Rider is part of a group lost in time and only the Mysterious Man can set it right, and only Emily can find out when the legend began. And there are forces at work trying to stop this last chance to save the victims of the time loop!