If there is a war between the US and China it will be because the US starts it.
The Chinese have a different attitude to war than we do, their attitudes are still based on the classic text "The Art of War" which is thousands of years old and is still taught in mainstream universities in China today as a way of strategic thinking in life and business as well as war. The Chinese mentality is to never get involved in a war unless they are certain of the outcome and are certain that it will leave them better off than before. They would never have done what we did and gone into Afghanistan / Iraq and then found out we didn't have an exit strategy. China will want to build up its military power to maintain its own security (but that is also driven by security concerns of their neighbours like India, its not just a message against the West) but the Chinese would always rather keep their heads down and live peacefully with other countries rather than have to divert resources into fighting. They also know that Chinese development depends on their advantage in being able to export to their huge markets of the USA and Europe, and they cannot afford these markets to be damaged.
I expect there will be frosty relations between the US and China but I don't see China aggressively asserting itself militarily, China will however extend its influence over the world but this will be by increasingly owning more and more assets in foreign countries, but each time they increase their assets abroad they give themselves a disincentive to damage that country's economy.
Bad human rights yes. Polluters yes. War mongers no.