(remember that any official media of the Chinese government or Communist Party are not really media in the sense that we know them. They are simply statements of government policy in the guise of news. They are useful in telling China watchers what the government and party thinks of many issues and events.)
China Daily (official Chinese government newspaper)
People's Daily (official paper of the Chinese Communist Party)
People’s Daily in English (if this doesn’t work go to the above Chinese link and find a link to the English version)
Taiwan Central News Agency (official government news agency; look down the left side of the page for the English version.)
Independent news on China and Taiwan
(independent media from regional and international sources)
Inside China (independent news on China, published by the European Internet Network)
China News Digest (independent news organization that compiles news on China from many sources; this is the best daily news source on what is going on in China)
South China Morning Post (the best English language daily newspaper in Hong Kong; still an independent newspaper to a certain extent, but it can be influenced by Chinese and Hong Kong governments. Their best political reporter on China, Willy Wo Lap Lam, was fired for being too critical of the Communist party)
Hong Kong Standard (also an excellent free and independent newspaper out of Hong Kong)
American Institute in Taiwan (The US government’s "Embassy" in Taiwan. It acts as an unofficial embassy, since the US and Taiwan have no official diplomatic relations.)
on Taiwan (produced by lobby groups or government-related organizations who want to make sure that Taiwan does not get marginalized and forgotten in the world's rush to gain access to the mainland Chinese market)
Security (issues related to China, Taiwan, and the US)
Think Tanks
Taiwan Security Research (Department of Political Science, National Taiwan University page which compiles everything written about Chinese, Taiwanese, and Northeast Asian security)