Definitely “My Side of the Mountain” by Jean Craighead George. In the same series is “On the Far Side of the Mountain” and “Frightful’s Mountain”
“Where the Red Fern Grows” by Wilson Rawls
Gary Paulsen’s “Hatchet” series… “Hatchet”, “Brians’s Return”, “Brian’s Winter”, “The River”, “Brian’s Hunt” (probably not in that order)
Gary Paulsen’s “Mr. Tucket” series… “Mr. Tucket”, “Call Me Francis Tucket”, “Tucket’s Ride”, “Tucket’s Gold”, “Tucket’s Home” (in that order), but don’t let him read these to himself…. read them aloud to him because they are THAT GOOD… I was always waiting for the end of the day so I could find out what happens next! Our library didn’t even have this series, but I interlibrary loaned them and eventually bought the ‘1-5 books in one volume’ (because I’ll want to read them to his 3 younger brothers too)
“Indian in the Cupboard” by Lynn Reid Banks… also in the series: “Return of the Indian”, “The Secret of the Indian”, “The Mystery of the Cupboard”, “The Key to the Indian” (probably not in that order)…. these were also a great hit and hard to put down.