For me I'm hoping for either Ben Whishaw or Kris Marshall! Kris just left Death in Paradise, sooo...Also be neat if it was a female...But I think I read something that confirmed the 13th Doctor was to be a male? Anyways, I'll miss Capaldi.

My choices are:
Tom Hiddleston (AKA Loki)
Robert Carlyle (AKA Gold in Once Upon a Time)
Tilda Swinton (AKA the Ancient One)
And Simon Pegg.
David Bowie would have been a great choice and there are people who want Rupert Grint aka Ron Weasley to be the next doctor although I am not sure about it.

Carlyle and Swinton would be cool choices. I was very much into Hayley Atwell (Agent Carter) until the rumour was debunked.