As for MP, I just finished the personal goal for Operation: Goliath - i.e. beat a Silver Reaper map and get at least one team mate extracted. I was not one of the people who got extracted because I got stuck on a ladder.
Not the first time that's happened, either...
I started out with an Asari Vanguard (unlocked her with my freebie starter pack), but I've grown dissatisfied with it. She seems to be a bit too ineffective against the really big stuff - particularly things that like you to get up close so that they can one-shot melee kill you (like Banshees, for instance... I *hate* those...). More recently I've been playing with a Turian Sentinel, and that's what I beat the Goliath challenge with. I find his Overload and Warp abilities to be very useful against the big nasties. Weapon unlocks are slow, for obvious reasons (gotta keep you playing!), but they're slowly coming along. I haven't received any Rare weapons yet, but I have unlocked a couple of the Rare race/class characters.