To get the most out of Single Player, you don't need anything but the stock game.
BF4: Game
Comes with original Single Player campaign, basic Multiplayer (Stock gamemodes, guns, etc.)
You must pay for all current and future DLC's unless you buy Premium.
Doesn't come with Premium items (such as some guns)
BF4: China Rising
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Adds 4 new multiplayer maps.
Air Superiority multiplayer Game Mode.
New multiplayer vehicles.
BF4: Premium
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Gives all future DLC's (including current China Rising) and those 12 Battlepacks.
If your planning on playing Multiplayer AT ALL I suggest getting the Premium package.
I did so for BF3 and it adds SO much to the game.
It's up to you though. The game was made for Multiplayer, but Singleplayer only, then just get the stock game, you are literally wasting your money otherwise.