I'm really looking forward to the Advanced Warfare campaign - it looks like they've really pushed the boat out for a spectacular story, locations and characters. I haven't really enjoyed a COD campaign since MW2 in all honesty - the last few have been pretty forgettable and typically more linear and generic than ever. The Black Ops 2 campaign was intriguing with the new gadgetry and essentially a Create a Class system where you could choose you're weapons, even from the past such as the Galil and AK47 but the missions, particuarly the Strike Force ones fell flat and became annoying. Ghosts was something new in terms of narrative but essentially the same old one-dimensional styling. The characters and locations were pretty lame although there were a couple of stand-out missions that looked and played pretty good.
Apart from Ghosts; I have done all the campaigns first and I definitely want to experience AW this way. I am not one of those that wants to reach Prestige 10 by December and think that rank means anything because it doesn't in COD.
I can't wait to see the multiplayer in action but I think the campaign is shaping up really well and shouldn't be overlooked. I absolutely loved COD 4 and MW2's for their memorable missions on stunning backdrops such as Cherbobyl and the Russian airport. It's so tempting to jump into the multiplayer from the off but I enjoyed COD back in the day when I gradually saw the entire product unfold and not overlooking features or flitting between the modes here, there and everywhere.
Campaign first for me, definitely!