I definitely want a brand new crew and companions. No familiar faces, no familiar names. I don't want Wrex's kid on my ship, I don't want a Drell whose ancestor was Kolyat Krios. I don't want Quarians, I don't want Geth. Geth were ruined in ME3 and Quarians ... well... let's just let this issue rest.
The are only two Asari I like. One is Aethyta because Krogan father, humour and being not a typical Asari. The other one is Aria. She is so awesome, I made a renegade female Shepard just for the Omega DLC. And after the kiss, back on the Citadel... I got drunk so I woke up sleeping next to Aria on the couch. I wonder if she thinks of Shepard as her pet now? 
Mordin was the only Salarian I liked.
Most Krogan are annoying brutes.
I expect at least two human companions, male and female. I am hoping for an attractive, intelligent, non-bigot, badass woman, perhaps a biotic. A little less chaotic than Jack, but with attitude. Not a stereotype like Ashley. And as long as the male isn't as boring as Kaidan, then I'm good. Perhaps some kind of scoundrel?
A Turian female would rock.
A Krogan who's into science, books and other nerd stuff.
Two companions from species native to Andromeda. Maybe something insectoid? Or a large bird?
I wouldn't want more than 6 companions, I don't want to spend half my time outfitting them.
They can put the obligatory Asari and Salarian on the crew of the ship, I don't really need them in my squad.