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Instead of a base on the moon a better idea might be a base inside the moon.
"Japan’s space agency said it had discovered an enormous cave beneath the lunar surface that could be turned into an exploration base for astronauts."
"The chasm, 50km (31 miles) long and 100 metres wide, appears to be structurally sound and its rocks may contain ice or water deposits that could be turned into fuel, according to data sent back by the orbiter, nicknamed Kaguya after the moon princess in a Japanese fairytale."
https://www.theguardian.com/science/2017/oct/19/lunar-cave-discovery-raises-hopes-for-human-colonisation-of-moon [theguardian.com]