Which currency is preferred when countries with different currencies purchase imports/sell exports? For example, when a company in the United States sells goods to a company or distributor in China, does the U.S. company accept payment in yuan (which it then exchanges for dollars on the currency market) or dollars? 

Likewise, when a Chinese company sells goods to an American company, does the Chinese company accept only yuan or will dollars suffice (even if they have to be sold to purchase yuan)? 

Are some currencies (for example, the dollar, British pound, or euro) preferred in lieu of weaker currencies when two parties are exporting/importing on the international market?
There isn't a typical answer.

The vendor may want paying in whatever currency represents the highest proportion of their costs, as this reduces their currency risk.

But there may also be restrictions on what currency they can trade in; how much of some particular currency they're allowed to hold; there may be capital controls in place; some currencies might be easier to hedge than others; trade in some currencies might attract that country's tax authorities, if significant movements have to be registered; ... and so on.

They might want to do business across various buyers in a basket of currencies, as a way to minimise currency risk through diversification.

They may prefer to do business in currencies with a higher liquidity (USD, GBP, EUR, CHF, AUD, JPY, CAD).

There are lots of variable factors in play. And it's a negotiation between vendor and buyer; the above is written as if the vendor holds all the power, but similar issues apply to the buyer too. For example, the buyer may want to pay in whatever currency represents the highest proportion of their income.