Tough call. Some countries I'd rule out because they've only become interesting recently, namely USA, Germany.

Australia shouldn't even be considered.

Spain perhaps for the whole South America deal, which IMO tops any of the 19thC European imperialism for overall influence/importance.

Eastern Europe has been a big political mess so I'm not sure what country you would be picking.

I know little of African history.

Canada is boring.

Ok I'm actually going for Russia. It has empire, revolution, religion, culture, literature, although most of the history available relates to the monarchy/clergy/upper classes, but that goes for most countries.

I'm no historian, but surely the answer has to be somewhere like Iraq. The cradle of civilisation, through the Sumerians, the Babylonians, the Assyrian empire, directly invovled in both Greek & Roman History then the golden age of Islamic science (Abbasid). while they have been relatively quite for the past 600 years, that is a short time in an 8000 year hisotry.

Britain, for all the reasons mentioned by other posters, however I have selected Germany as my second choice. The impact of two world wars has had arguably the largest single impact on the modern political structure of the world.

The fact that Greek thinkers were the unquestioned intellectual authorities, not only in the west but also in Islamic culture, all the way until Descartes puts them at the top of my list.