Ideally, a spin-off should be different enough from the original series and this would be easily accomplished with 'The Paternoster Gang'. (If you can think of a better name for the show, let me know!)
It would be set in the Victorian London of the mid-1890's as its base of operations (but could go off to the countryside or even to other countries, perhaps once or twice off-world.) In general, the show's tone would be that of "steam-punk".
The villains they encountered could be aliens, but should only be one at a time, at best a handful, and not some invading force that could draw attention to itself and disrupt the similar timeline between Toobworld and the Trueniverse.
So hopefully that would leave out the over-used Daleks and Cybermen. But perhaps another Sontaran warrior to spur conflict in Strax's loyalties? And there are plenty of alien species seen in the three other Whovian shows who could supply an individual to pose a threat to the British Empire and the world.
Mostly, however, I think it would work best when the Paternoster Gang deals with home-grown threats - the mad scientists, the power-hungry nobles, Jack the Ripper wannabes, foreign spies, and explorers possessed by ancient spirits unleashed from archaeological digs - the kinds of pulp fictional characters you would find in the 'Ripping Yarns' of the time.
(I think 'The Wild, Wild West' would serve as a wonderful blueprint for the series, in regards to the steam-powered weapons of destruction and the mad men - and women! - who would deploy them.)
Plus there would historical figures they could interact with: Queen Victoria, of course (And wouldn't it be grand if Pauline Collins could assume the role once more?), Gladstone, Kipling, Lillie Langtry, Gandhi (during a trip to South Africa), Sarah Bernhardt, and Bertie the Prince of Wales.......
And finally, not only could there be a guest shot by the Doctor (perhaps in the first episode to properly kick it off), but the Torchwood organization could make recurring appearances as both an adversary and ally. And of course that would mean we couldn't rule out a visit by John Barrowman as Jack Harkness.
Let me know what you think......