The full reward order

Activision lists these rewards “in order” of completion. Park, the playable protagonist, is the final unlock.

MW4 campaign completion rewards in order
#RewardType
1ChoBase Operator
2No More RulesCalling Card
3Double XP TokenXP token
4DallasBase Operator
5Ready LineLoading Screen
6LucaBase Operator
7Gone DarkEmblem
8Oh-JiBase Operator
9Double XP TokenXP token
10KalBase Operator
11Double Weapon XP TokenXP token
12DunnBase Operator
13Double Weapon XP TokenXP token
14WestBase Operator
15Double XP TokenXP token
16ParkBase Operator

What the campaign actually covers

Sixteen missions span the Korean Peninsula, Paris, New York and Mumbai. You play Private Park Hyun Jun defending against a full-scale invasion while John Price hunts the person pulling the strings. Campaign progress is separate from the DMZ Early Access window that starts October 20.

Do the rewards carry into DMZ and Multiplayer?

Yes. Activision states the rewards “will be available for use in Multiplayer and DMZ upon the full game launch.” Because DMZ Early Access opens October 20, expect the Operator unlocks to become selectable on October 23 rather than during the early window.