Gaetti played collegiate baseball for Lake Land College in Mattoon, Illinois and Northwest Missouri State University. Legend has it that Gaetti holds the record for the longest home run in NWMSU baseball history, an estimated 505 foot home run. Gaetti was drafted three times before finally signing with the Twins: first by the St. Louis Cardinals in the fourth round of the 1978 Major League Baseball draft (then held annually in January) and again in 1978 by the Chicago White Sox in the third round of the June secondary draft before he was drafted by the Twins in the first round of the June secondary portion of the 1979 draft. Gaetti signed on June 21, 1979.