I’m sure I read this when I was a teenager. I read a lot of Heinlein at the time.

It’s a young adult classic.

Have Space Suit—Will Travel … was nominated for a Hugo Award in 1959 and won the Sequoyah Children’s Book Award for 1961. …

High school senior Clifford “Kip” Russell is determined to get to the Moon, but the price of a ticket is far beyond his reach. His father suggests he enter an advertising jingle-writing contest; first prize is an all-expenses-paid trip there. Instead, he wins a used space suit. 

… He is shocked when a flying saucer lands practically on top of him. An 11-year-old girl (Peewee) and an alien being (the “Mother Thing”) flee from it, but all three are quickly captured and taken to the Moon. …