Something I'd like to see is the player character NOT be already in charge of everything, like how Shepard was merely the "XO" (second-in-command) in ME1.
That way, you could have someone else in authority give the player an order to investigate something or other:
"I need you, Cora, and Drack to investigate the engine room of the Ark! We haven't heard from them in some time and their radios seem to be down."
- Who's Cora?
"She's a biotic, one of the best on the ship. She can help lock things down if the gravity generator is out.
- Who's Drack?
"A krogan, and a tough one at that. He's one of the best mechanics on this ship, so if something's wrong with the engine, he'll know how to fix it."
- All right, I'll find them. We'll make sure the ship is safe.
"That's good to hear, now find out what happened and report back ASAP."
- I don't need them, I can handle this on my own.
"I appreciate your confidence, but this isn't a solo job. Find out what happened and report back ASAP."
The idea is that you and your starting companions are more-or-less thrown together on the spot.
It's also an easy way to put in dialogue for the player, to let them find out more about who's who, as well as establish a precedent for Paragon/Renegade leanings.