This was originally the first one on the list, but the season opener had to go in front really.
3: Stumbling Into History (without aliens)
The "historical" seems like a sensible place to start even though there hasn't been one in about thirty years, as it was the original model for the series, as set by An Unearthly Child.
The travellers step out of the TARDIS and run into events from Earth's history, which doesn't go quite as expected...
This could be a "celebrity historical" where the travellers bump into someone from the history books, or the characters they meet could be "ordinary" folks of the period. A good bet for an interesting adventure (rather than an interesting history lesson) would be one of the unsolved questions of history. And since we're playing fair, the solution isn't "aliens did it". Another alternative would be the sort of historical event that blockbusters get made about, like the Titanic or, indeed, Pompeii.
Travellers getting mixed up in historical events is the norm for non-Who time travel stories, so you shouldn't have much trouble thinking of the kinds of things that can happen:
The travellers land, and either something piques their interest or they're separated from the TARDIS, so they have to stick around for the rest of the story.
The writer shows off obscure historical knowledge and/or use of Wikipedia and the audience learns some historical facts in an entertaining way, thus excusing this alien-fighting palaver as public service broadcasting.
Someone realises that something of great historical import is about to happen, and that "great historical import" generally means the people in the middle getting hurt or killed. Jeopardy and possible "can't we save them?" angst.
A character annoys the locals by being anachronistic - trying to interfere with the impending disaster, mouthing off to a feudal lord, dressing inappropriately - and this leads to a scuffle with the goons of the period, possibly some running, and optionally being captured and thrown in a dungeon.
Someone changes into period costume to blend in better. The First Doctor and companions did this way more than later ones who tend more to "just walk round like you own the place." This may lead to cases of mistaken identity and/or travellers with potential romantic interests seeing the dressed up traveller in a new light.
The travellers team up with sympathetic locals to deal with the threat at hand.
The mystery is solved, the villain is revealed, the disaster occurs, and there's an awful lot of running to do.
The characters get back to the TARDIS and the trailer for next week shows them in space to demonstrate contrast.
The TARDIS lands in Jerusalem in 1187 AD, under siege by the armies of Ṣalāḥ ad-Dīn. Almost immediately chased as suspected spies, they escape in the confusion but the TARDIS is inside one of the keeps, difficult to get to... and the siege ends tomorrow.
Between trying to find a way back to the TARDIS, dealing with the internal politics of the collapsing Kingdom of Jerusalem and various forces trying to control it on both sides of the wall, the travellers have plenty of opportunities to get in trouble, discover historical facts, debunk myths about the Knights Templar, disguise themselves as knights and damsels, mess up history, stop someone else messing up history, brood over how many people they now know must die so that history can take its proper course, look at the siege from all sides, and do some running.