Get Mass Effect 1,2 and 3.
The story has to be the best I have ever encountered in any video game. The feelings and the choices you have to make are just fantastic, and it puts you as a player deep within their universe, their world. I just wandered around, enjoying those small but perfect details.
Sure, Mass Effect 1 was the best in my opinion, and it was the real RPG out of the series. Mass effect 2 is more casual with less RPG elements, and so far it seems to be going into a even more casual direction with Mass Effect 3. But I simply ignored that and just enjoyed the story. You transfer the save from your previous game, so all your choices, all your companions, everything follows you. It was like that in Dragon Age as well, but that can't really compare to the amount of role this feature plays in this game.
I also recommend to get as much DLC as you can. And you should refrain from looking up stuff on the internet, spoilers is a bitch.