The main language systems are
Austroasiatic includes Mon (Burma), Vietnamese and Khmer.
I have done a post on Austronesia. Austronesian languages include Malay, Polynesian languages and Tagalog.
Hmong-Mien languages are spoken in mountainous areas of southern China. Within the last 3-400 years, many Hmong and Mien speakers have migrated to Burma, Thailand, Laos and Vietnam.
Sino-Tibetan includes Chinese (Mandarin and non-Mandarin), Burmese and the Tibetic languages. It has more native speakers than any other language family except the Indo-European. Tibeto-Burman refers to the Sino-Tibetan languages that are not Chinese.
Tai-Kadai includes Lao and Thai (last post).
These are linguistic, not ethnic, classifications.
African languages (old post).