There are no adds in-game whether you buy the retail box or download from origin, and you must install origin to play the game, so the point is moot anyway. There is a DLC tab on the client, but it is unobtrusive. I think you can disable it if you want to, but if you just ignore it it won't bother you. When you first boot up origin or your PC, you might get a pop up window with offers from origin, but it's not an invasive one. You can just close it. I think that can be turned off in options though. I don't bother because it behaves itself.
The nice thing about origin is that once you install a game, you will always have access to it. If you switch to a new PC you can re download it without having to find your disk. I'm actually beginning to like origin better than steam now. I'll admit that I hated it at first, but they've ironed out the things I didn't like.