Note: all of these topics/categories can be found in multiple sources, so don't think anything listed here is remotely comprehensive! You may also find that its easier to get context for data through sources like scholarly books and articles. Need older data than what is available online? Many online statistical databases started out as books published by international organizations - look for them by title in Search It (i.e. CIA World Factbook or the Human Development report/Index).
IMF Statistics are mentioned a lot here; check out this matrix for what resource/database has what information.
Start with the Background Resources tab - these sources will give basic information about things like when/if a country becomes independent, major governmental changes (i.e. dictators, revolutions, democratic government happens, etc), major economic events, etc. You can also look at books that provide general histories of particular countries, or look them up in online reference sources.
World Trade Organization, including their publication Doing Business: Measuring Business Regulation; Investopedia's Primer on Currency Regimes (exchange rates). Note: Please use your phone to take pictures of any pages from the PRY and other reference books, rather than checking the volumes out!
International Monetary Fund (see: https://www.imf.org/external/NP/mfd/er/index.aspx)
Look under the big international organization (i.e. UN, World Bank, OECD, etc) "topic" links for general categories.