Definitely a kart racer.
Not a spritual successor to Diddy Kong Racing -- why another spiritual successor? Their next game should stand on its own; sure, it'll probably be inspired in part by their past games, but Playtonic should begin to establish themselves in their own right.
I absolutely adore Mario Kart and would love to see Playtonic's go at a similar game, using their beautiful worlds, characters, humour and innovation. Mario Kart 8 had anti-gravity; I wonder what Playtonic could come up with? Perhaps, as Yavga said, some sort of platforming elements could be interesting, though I can't immediately think how it'd work. The possibilities are really exciting though.
I loved Perfect Dark. The story was incredible, but I can't see Playtonic's current characters fitting in with a 'realistic' shooter like PD. They will likely need to come up with new characters for something like that to work, and that would kind of create a second Playtonic universe as I can't imagine those worlds meeting. It'll be like Joanna meeting Banjo and Kazooie -- wouldn't work.