Hell yes. I absolutely love trophies - they encourage me to experience a game to its fullest extent, which, in my opinion, is a good thing. As an example, I'm not a huge fan of multiplayer, but as a result of most games having trophies related to multiplayer, I end up playing that mode anyway, and in some cases end up having quite a bit of fun with it (Bioshock 2 would be a good example). I'm on the verge of getting my 25th platinum (Batman: Arkham Asylum), and I have no intention of stopping anytime soon.
However, one thing I won't do is go out and buy a game just to get the trophies - I feel that is flat-out stupid. Another thing I won't do is let myself get bothered by the fact that many games don't read "100%" completed after getting the platinum trophy due to DLC. If I really enjoyed the game, then by all means, I'll download the DLC. However, in the case of games such as Black Ops, Bioshock 2, or Resident Evil 5, I'll be damned if I'm going to pay anymore for what were incredibly average games in the first place.
To answer the OP's question, this is what I did with MW2: play through the game on normal difficulty the first time around, picking up what achievements I can. The second run will be the difficulty-based, collectibles run. As for the Spec Ops challenges, those will be played on Veteran the first time around. They're meant to be challenges, after all.