Hicks skipped a family cruise to Jamaica to get into uniform and meet players Monday. Plummer said he wanted to be in the majors in two or three years.
The Cardinals have signed six of their 12 picks in the first 10 rounds as well as three non-drafted free agents. The team had reached terms with 19 players overall.
Plummer, Woodford and Hicks all were signed out of high school. Plummer, the 23rd overall pick, is a center fielder. Woodford, the 39th pick, and Hicks, pick 105, are both right-handed pitchers.