With regard to China: China's preferred strategy is to intimidate liberal US presidents.
China's strategy is multi-pronged. The main strategic aim of the PRC is to become the pre-eminent power in East Asia. This includes subsidiary goals of:
1. Bringing Taiwan into the mainland control.
2. Keeping Japan as de-militarized as possible.
3. Prevent collapse of North Korea and possible stationing of American troops on the Manchurian-Korean border.
4. Domination of the South China Sea.
5. Developing hegemonic influence over Southeast Asia, particularly those with large or influential ethnic Chinese population (Vietnam, Thailand, Singapore, Malaysia, Indonesia and Burma).
Chinese leaders do believe that a conflict with the US might be possible in the future, because their aim of the Chinese pre-eminence in Asia will be in conflict with the traditional American objective of preventing the rise of continental powers.
In regard to the US, their goal is to derive maximum commercial, economic and scientific advantage from the trading relationship while they build up their military-industrial base. A military conflict with the US is to be avoided at all costs at least until Chinese military-industrialization reaches a certain point where the PLA has a semblance of technological parity with the US forces.
With regard to China: China's preferred strategy is to intimidate liberal US presidents. They don't like President Bush, because they can't intimidate him, and they sure don't want the NK's starting some sort of a war right now. I expect them to come down as hard as neccessary to keep the NKs from nuking Japan or some such, at least until we end up with another wimp liberal in the White House.
It can be argued that the Chinese have derived benefits from Republican administrations as well as from Democratic ones. A number of prominent Republican policymakers and power-brokers (including Henry Kissinger) maintain unhealthy commercial relationships with key figures and politico-economic entities in China.
Then there is the odd coalition of Republicans who oppose China on moral-strategic ground and Democrats who oppose China on economic-protectionist grounds.