The official language of the state is Burmese. Like Chinese, it's a tonal language, so the same word can have different meanings depending on the tone with which it is said.
Its alphabet was adapted from Brahmi (Indian) scripts which came into the country together with the Buddhist religion. With its letters mainly modelled on circles and segments of a circle, it's instantly recognisable - but not easy for foreigners to read.
You'll be fine in most places with English, particularly speaking to younger people. But if you only learn one word of Burmese, it should be mingulaba - 'hello'. Greet people with a happy mingulaba and you'll always get a smile back.