Reno Bertoia came to Minnesota with the Twins in 1961, and brought the number he had worn with the Senators along in his suitcase. (Born in Italy as "Pierino," he is the only "Reno" to play in MLB.) Bertoia was the starting third baseman in the Twins' first game; they defeated the Yankees 6-0 at Old Yankee Stadium. He played 35 games, then was traded on 01 June with Golden Gopher Heismann runner-up Paul Giel — a native of Winona, Minn — to Kansas City. The same day, Milwaukee traded Billy Martin to the Twins. Both men were listed at 5' 11"; Martin took over the number. While Martin has more to his story than just that, both men are exemplars of one of the primary types of player to wear this number: banjo-hitting infielders. Another group — banjo-hitting, fleet-footed outfielders — reached its fullest expression in the late Eighties to late Nineties.
Martin, of course, is known best for his exploits & altercations while manager of the '69 Twins, who finished first in the new AL West during his only year at the helm. Much could be said about Billy Martin; suffice it to say he's a significant character in the story of the Twins' greatest period of dominance.
No Twin wore Nº 1 in 1962, but after Bernie Allen picked it back up midway through the 1963 season, the number stayed in circulation until 1970. Eric Soderholm wore it for two seasons with a 72 OPS+ over 391 PA, then switched numbers and put up a 117 OPS+ over his last remaining 1136 PA as a Twin. The guys who came after Soderholm didn't find any better success wearing it, and then Twins didn't issue the number to anyone in 1979. In 1982, Ray Smith became the first — and so far, only — catcher to wear Nº 1 for the Twins.
After another break in 1987, John Moses was issued the number and started the above-mentioned run of fast, light-hitting outfielders that ended with Otis Nixon. Moses had his career year in '88, an okay year in '89, and, along with the rest of the team, crashed to Earth hard in '90. Jarvis Brown wore Nº 1 in 1991. Had Gene Larkin not pinch-hit for him in the bottom of the tenth in Game 7, Brown might be the least-remembered position player on the Twins '91 World Series roster. (We'll get to the guy who could claim that title later in this series.) Alex Cole brought Nº 1 back into circulation with a solid year in 1994, batting .296/.375/.403 (102 OPS+) over 398 PA, with 15 doubles, 5 triples, and 29 stolen bases (78% success rate). Cole was the Twins' first primary center fielder following Kirby's move to right field, but unfortunately for him, his incumbency lasted only lasted one year. He was off to a solid start in 1995, but must've gotten injured; he missed every game from 01 June through 22 September, and apparently did not play in the minors. Three seasons later, Nº 1 was issued to Otis Nixon, who had worn the same number in Atlanta. By the time he reached the Twins, Nixon was just two years younger than Billy Martin was when he became the manager of the 1969 Twins. Nixon stole 37 bases — with an 84% success rate! — for the Twins, which nearly doubled the franchise's previous high water mark for a player 39 years old or older. (Lave Cross stole 19 bases in his age 40 season for the 1906 Senators. Paul Molitor held the post-relocation record, with 18 in 1996.)
The past twenty years have seen Nº 1 alternate between Gardenhire-era second basemen and fifth outfielders — with one exception: Jason Kubel wore it as a September call-up by the 2004 Twins. Kubel looked really impressive, hitting .300/.358/.433 (.320 BAbip, 104 OPS+) over 67 PA. He was 22. After that first cup of coffee, Kubel blew out his knee in the Arizona Fall League. When he returned to the Twins in 2006, he did so wearing a different number. One wonders what might have been.
Whether Kubel wanted a new number or not, part of the reason he wasn't reissued Nº 1 was that Luis Castillo was wearing it. Castillo came to Minnesota in a December 2005 trade from Florida — where he had worn 1 since 1997 — to fill what had been a gaping hole for the Twins since the Chuck Knoblauch trade. Castillo put up 2.3 rWAR for the best post-Knoblauch season at the keystone in his first year, and followed it up with 1.4 rWAR the next before a deadline deal sent him to the Mets. The Twins proceeded to flail around again until Orlando Hudson signed a one-year free agent deal for 2010. O-Hud put up the best single season for the № 1 jersey (in what remains the single best post-Knoblauch season at second base), and the Twins won 94 games and repeated as AL Central champs in their first year in Target Field. Hudson was allowed to walk after the season, which turned out to be his last decent year. He was known to be a chatterbox, and — if Poultry Man is a credible source — complete wore out his welcome. The Twins elected to assign № 1 to their new second baseman, Tsuyoshi Nishioka, who came over from the Chiba Lotte Marines. Nishioka had won the batting title in his last year in Japan, which lended some excitement to the Twins' first acquisition from NPB. Six games into the season, Nick Swisher broke Nishioka's left fibula with a takeout slide. Nishioka missed all of May and half of June. The Twins lost 99 games, and General Manager Bill Smith was fired in November. After a poor showing in 2012, Nishioka asked for and was given his release, despite having a third year left on his contract. He returned to Japan and played for the Hanshin Tigers until 2018.
Nick Gordon wears № 1 for the Rochester Red Wings. He appears to be the successor to the Punch and Judy infielder line, but his future in the organization is more doubtful than his draft number once suggested. The frequency with which the Nº 1 is assigned to players has also dropped since its near-ubiquity from 1961–1995. Whether this is incidental or by design is hard to say. There are only ten single-digit numbers, and the Twins have already retired three of them. Whether the Twins have gotten more selective about who gets them remains to be seen in future installments.