I looked at the DLCs and I think Back to Karkand looks like the DLC that you should buy first. From what I've seen, the maps are huge and allow you to use vehicles. Close Quarters on the other hand, I saw the maps and while I do think that they look good since they are just like the map pack suggests and I don't think that they are as good as the Back to Karkand maps. As for the new Conquest mode in Close Quarters, I really haven't seen much and I am going to guess that Conquest mode is capturing territories and that the game doesn't end until either all terroritories are captured or time runs out (Not for sure).
Overall I say that you should probably go with the Back to Karkand pack first.