Rodriguez--also known as "Pudge" or "I-Rod"--gave thirteen of his best seasons to the Rangers between 1991 and 2002. During that span, he made ten consecutive All-Star appearances and won the same number of Gold Gloves. He retired with thirteen Gold Glove Awards altogether--more than any catcher in history. His offense improved as time wore on and he reached the peak of his career in '99 with 35 homers, 113 RBIs and a .332 batting average--numbers good enough to capture MVP honors. After his departure from Texas in 2003, he led two other clubs to World Series appearances. He was named MVP of the 2003 NLCS and compiled a .313 postseason batting average during the Marlins championship run that year. Behind the plate, he had an accurate arm and quick release. He led the league in caught stealing percentage nine times. His is the all-time leader in putouts among catchers.
It would be just as easy to name Jeff Bagwell the top Astros player of all time, but I chose Biggio because he gave twenty seasons to the club as opposed to Bagwell's fifteen. Biggio started his career as a catcher and spent a fair amount of time in the outfield before making the switch to second base in 1992. The position suited him well as he led the NL in assists six times and putouts on five occasions. He captured four Gold Gloves. One of Biggio's most useful talents was getting on base. He drew 60 or more walks ten times and led the league in hit-by-pitch during five seasons. He wore an over-sized elbow guard and had a tendency to lean out over the plate. Only one other player was plunked more times than Biggio--Hall of Famer Hughie Jennings. Biggio had excellent speed, stealing more than 400 bases during his career. He led the league in 1994. His 3060 base hits secured him a place in the Hall of Fame. He was elected in 2015.
Had Nolan Ryan remained in an Angels uniform a bit longer, he would likely have broken every franchise pitching record. But in examining the team data, the player who really stands out is left-hander Chuck Finley. During his fourteen years with the club, Finley set franchise records for wins and innings pitched. He ranks second behind Ryan in strikeouts. Highly durable, Finley made 30 or more starts eleven times during his career. He led the AL with 13 complete games during the '93 slate. The Angels weren't particularly good during many of Finley's seasons, but he was a model of consistency almost every year. He had several good pitches in his arsenal, including a fastball, forkball and curve. An unusual claim to fame, he struck out four batters in an inning three times. Throughout his career, he maintained a sense of humor about himself. After being named Player of the Week one year, he quipped: "That just shows you how this league has gone to hell."
Ken Griffey Jr.
Though Ichiro Suzuki and Edgar Martinez put up impressive stats over the years, Griffey Jr. was a better player all around. With more power than Ichiro and more versatility than Martinez, Griffey led the league in homers four times and captured ten straight Gold Gloves. He got started in the majors at the age of nineteen and demonstrated so much poise, he was nicknamed "The Natural." He retired with 630 career homers--placing him sixth on the all time list. He accomplished this presumably without the aid of steroids. He holds the record for most homers in a season by a center fielder (56--tied with Hack Wilson). He captured more than ninety percent of the Hall of Fame vote in 2016.
The A's have resided in three different cities over the years, spending more than fifty seasons in Philadelphia and close to fifty more in Oakland after a brief layover in Kansas City. During the Philadelphia years, pitcher Eddie Plank was arguably the most valuable asset to the club. The first left-hander to win 300 games, "Gettysburg Eddie" was a workhorse for manager Connie Mack, averaging 20 wins per year between 1901 and 1914. He accrued a stellar 2.39 ERA in that span while leading the AL in shutouts twice. Plank was even better in the postseason, allowing just 8 earned runs in 6 World Series starts. A victim of poor run support, he won just two of those starts in spite of a miserly 1.32 ERA.
During the Oakland era, nobody carried the club like Rickey Henderson. The greatest leadoff man in history, Henderson is the all time leader in runs scored and stolen bases. He ranks second in bases on balls. Though he remained in the game long after his prime, he still manged to retire with an on-base percentage above .400. Henderson had some power for a leadoff man, cracking 297 career homers. He holds the record for most homers leading off a game with 81. Imminently aware of his abilities, he often bragged about his on-field accomplishments while referring to himself in the third person. In a story he vehemently denied, he allegedly left a message on the answering machine of Padres' GM Kevin Towers saying: "This is Rickey calling on behalf of Rickey. Rickey wants to play ball."