It is all specualtion at this point but based on previous games I would say you need to do the following.
1) You need to win.
2) You need to finish at the top of the scoreboard.
The winning team gets the most match bonus and the higher you are on the leaderboard the more bonus you get. The higher you are on the leaderboard the more in game EXP you get as well.
I would rather get higher bonuses for playing well than trying out different weapons and stuff to pop the lower 500 XP challenges. I can get more EXP when I am using weapons that are better for my playstyle by getting more kills and relying on points 1 & 2 above.
I personally think objective games are better for ranking up fast. They provide natural points of conflict where as games like TDM are based entirely on where you are vs. the enemy (which may be on the other side of the map most of the time).
In BO I would play HC CTF. Tons of kills, and capture and defend points to rank up.
In MW3 I played a lot of KC. Our system was to have player A get the kill and then defend the tag while player B ran in to get the tag. This maxamizes the EXP available. The slayer ends up with the normal 100 EXP per kill but the tag runner would get the extra points for getting the tag.
However, when I had double EXP I would always play S&D. In MW3, it only counted the minutes you were actually alive in game. So if you stood around in a TDM game and got 10 kills x 200 points = 2,000 EXP you would waste 10 min of double EXP. However if you were to get 5 kills x 1,000 points = 5,000 EXP and you may have only been alive 5 minutes preserving 5 additional minutes of double EXP.
When it comes to weapons and other challenges I use the same stuff (weapons, streaks, etc).
The 10,000 EXP bumps when you hit 500 kills etc are easy ways to increase your rank and can cut 3-4 games out of a prestige run.
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