Okay, 1. Complete Challenges. You would get, I believe 41,600 xp if you completed all of the weapon challenges, (Marksman and Expert), plus a lot more for the Boot Camp, Operations, Killer, Humiliation and Elite challenges. I'm not too sure on the total xp you can gain from all.
2. Play HQ. Headquarters is a great game mode to get kills and points. Even though kills are only 5xp each, you can get over 40 on average. You also 15 xp for capturing OR destroying an enemy HQ, and you get 5 xp every few seconds for having the HQ captured.
Sabotage. I got nearly 1000xp playing sabotage. Well if you subtract 500xp for challenges and match bonus, it's 500xp. Headquarters is alright if you control the hq. if you don't it's a waste. In sabotage enemy's stay around the objective so there's 3 kills there, UAV. Throw a grenade into a building, 2 more kills. Air strike. 2 more kills. Chopper. On ps3 that's 20xp a kill. Around 150xp. You can also get a fab match bonus.