I'd like a system similar to Dragon Age Origins, where we get a separate origin depending on what species we choose to play as. A quarian would be leaving on pilgrimage for example, or a turian would be a C-Sec enforcer, or a batarian would be working security for Aria on Omega. Either way, whoever we play as, we end up serving aboard a rust bucket ship, running jobs on the slightly illegal side.
Basically, it should be the Mass Effect version of Firefly, to give us a glimpse of the less glamourous side of galactic life, moreso than ME2 showed us. A darker tone would be nice too, sort of a cross between the current ME visual style, crossed with the new Deus Ex colour scheme in places.
As for the ship, it could be something like a converted garbage scow. While I'd love for them to introduce a space flight mechanic like Freelancer or the X games, but that's highly unlikely, so the galaxy map should make a return, but it should look more run down, possibly flickering at times.