The doctor travelling with a male companion would be something new (I know he has done it before but not for extended periods) and someone from the past/future would be a change, but really they just have to have personality and not be annoying.
Not for extended periods? Jamie McCrimmon, anyone?
Sorry I thought it was fairly implicit that I was talking about the Doctor travelling
solely with a male companion. Others will know better but the only occasions that come to mind are the Doctor and Adric in The Keeper of Traken (I know Nyssa was there but my understanding is that Sarah was just a guest star at the time rather than a potential new companion) or with Wilf in The End of Time. Obviously he was travelling alone Jamie at the start of Evil of the Daleks and The Wheel in space, with Adric at the start of Logopolis and with Turlough at the start of Planet of Fire, but in each case new, female, companions were introduced in those episodes.
Unless I'm missing something painfully obvious?