I suppose the best place to start would be with those players selected in the expansion draft, though not all of them went on to play on the big team.
The 1960 MLB Expansion Draft was held by Major League Baseball on December 14, 1960 to fill the rosters of the Los Angeles Angels and the Washington Senators. The Angels and the Senators (who later became the Texas Rangers) were the new franchises which would enter the league in the 1961 season.
Each existing American League club had to make available for the draft seven players on their active roster on August 31, 1960, and eight others from their forty-man roster. The expansion clubs paid $75,000 for each of 28 players they drafted with a maximum of seven players drafted from each existing club, not including minor league selections. They were required to take at least ten pitchers, two catchers, six infielders, and four outfielders. The clubs also had the option of drafting one non-roster player for $25,000 from each established franchise.
So with that, lets dig in and start with the Angels #1 pick in that draft, Eli Grba.