Unbound might be best. There's too many stories over the decades, which ultimately all conflict against one another for a solid single continuity as such?
There were probably people in the 1970s who loathed the "12 regeneration cycle" as it imposed an end date to the show itself, and originally the regeneration concept was "a part of the TARDIS" ("The Power of the Daleks"). Even more fun, the 70s were also responsible for changing the cause of regeneration from a technological aid to that of an internal biological function, getting expanded on to creative effect in the 80s as a plot point with "Mawdryn Undead" and "The Five Doctors", and complete with handy "We'll give you a new life cycle" to the Master as a "let's get out of this dumb decision that was imposed that will hurt the show one day" card.
As for the police box shape, the ship arrived in a time when police boxes were normal, stored the pattern, ship left, ship came back later with the systems already breaking down (e.g. the old joke about the error detection system being damaged), but finally breaks down completely, remaining stuck in that shape when Susan was surprised that it didn't change shape. If the Doctor stole the ship because it was needing repairs, the repairs aspect being told in the 70s (but the stealing of it was revealed in "The War Games", the story that was otherwise to end the show with a bookend due to the show being too complex to make with budget and failing script concerns, but it got renewed but back to the other fun point, now imagine Hartnell's incarnation sneaking around out of boredom to go visit all of those planets and eons of time*,**), the ship already had problems and the camouflage unit may have been on the repair list already since Susan also indicated the ship was in the visage of a chair, an arguably illogical if not outright stupid design because (a) where's the door, (b) how does one get into it, (c) does one sit on it at which point can any old sod get inside if the operator forgot to lock the cushion?
* based on an action in "The Crusades", it's surprisingly not implausible**
** now that I realized that while typing that