I'm hoping for a pair of companions, male and female. Not as a couple, but could develop into a couple as the season goes along. I think having a second companion takes some of the pressure off the Doctor having to adventure directly with his companion at all times. Bill and Nardole as a team separate from the Doctor but moving towards the same end-game was a lot of fun and seriously was not used enough in my opinion. This dynamic could give the new Doctor a good amount of solo time as we get to know her. I'm also a sucker for some romance, so pairing them up over time would satisfy that and keep any lovey-dovey stuff away from the Doctor herself.
I think starting right off the bat with the Doctor having a single male companion to continue the male/female tradition would be too easy (albeit different) from a storytelling standpoint. It has the potential of turning into, 'Now its a guy that has a crush on her! What sort of hilarious mishaps and misunderstandings can come from this!' This is a worse case scenario mind you.. I doubt the new team will fall into something so predictable so fast, but you never know.
I'd like a chance to see how she works with both a male and a female, and how they would act off of her. I would also like them to both be full-fledged companions, as oppose to Amy the primary and Rory the secondary (I personally always consider him a side character, as he is defined by his relationship to Amy as oppose to his relationship to the Doctor). That could lead into a companion team leaving the Doctor at the end of the season as their own choice, something that doesn't happen enough. But at the same time, I wouldn't mind seeing a solo female or maybe a pair of female companions, because an all-female Tardis team does sound awesome.