I would think we would get something along the lines of Mass Effect 3, but obviously different.
No, there is no chance for other players to join your singleplayer campaign like Watch Dogs or things like this. YOU are the Inquisitor.
On the other hand I highly doubt we will get PVP, I just don't see the combat being viable in PvP situations. Unless its some form of duels. But why add duels and then call it multiplayer?
The Mass Effect 3 road is probably the most likely, or different forms of this. You make a soldier, you chose race and class just like OP said. And then you fight things. In what form will the combat be? I have no idea. It could be just like ME3 where you fight waves of enemies, or perhaps a more adventure version where you go through something. A cave of enemies, a battlefield or whatever, you name it.
I will be doing a lot of multiplayer, because its nice to keep playing the game but you don't have to focus on a questline or worrying about paying attention to things. Sometimes its just nice to sit on skype and kill things in a game you really do enjoy playing. Without having any negative sides of them interrupting you while you watch some important story parts in your game. Plus its nice to share a game you love with other people.
Of course we buy Dragon Age and Mass Effect for the singleplayer experience, but I feel the multiplayer is just extra features. Its fun plus BioWare will make a lot more money on having it. (if it has have micro transactions). And as long as it doesn't effect the singleplayer experience i see no problem with having it there. Refusing to playing it on principle is a bit silly I would say, but that is what I think.
I hope they do a bit more with it than endless waves of killing, and i have hopes that there is more. Why? Because I don't mind being a BioWare fanboy. 