Price attended Dallas Sports Academy (TX), a sports-oriented independent high school, where he played right field for the Bats in his senior year. He was named NAHS Most Valuable Player for their Independent Schools Conference, after posting a league-leading .444 batting average, along with 18 home runs and 58 RBIs.
During his senior year, in 2017, he was named Player of the Week twice, was voted to the All-Star team in the league's only All-Star Game held in the inaugural year, and was Batter of the Month for March.
On June 17, 2017, he was drafted first overall by the Battle Creek Attack (which later relocated and renamed to the Louisville Sluggers). He signed to the club for a signing bonus of $6,600,000, the highest-ever bonus signed by a player drafted into the Bull League.
He made his professional debut with the Clearwater Sluggers on April 17, 2018, going 2-for-4 against the Naples Admirals and scoring two runs in the team's opening day 11-8 loss. He got his first hit off Jimmy Buell in the top of the 4th inning, on a single to left field.