Frank Thomas figures to enter the Hall of Fame the first chance he gets in 2014. He's got the numbers, he's got the reputation, and a pretty good nickname doesn't hurt.
After that, it's hard to conceive of who the next player going into the Hall with a White Sox cap would be.
Pure his essential nature, there's nothing gaudy about Mark Buehrle's career resume, and while Paul Konerko has been a very good hitter, that's the only area of the sport where he's above-average, and really only started mashing at elite levels last season.
All the more reason White Sox fans should be clamoring extra hard for 85 year-old Minnie Minoso's last chance to be voted into the Hall of Fame, by way of a final candidacy through the Veteran's Committee this winter. Just like Minnie, Sox fans can't be sure when they'll get another opportunity to see the team get the greatest representation of all (besides the previously mentioned greatest hitter in franchise history, of course).
If that's not sufficient though, one could fall back on the "Minoso deserves it" angle.
As you can imagine is the case for an otherwise colorful and renowned figure standing outside of the Hall looking in, Minoso's stats aren't quite there.
On Bill James' Hall of Fame Monitor scale to calculate the likeliness of induction (with 100 being "likely" and 130 being "a lock") Minoso rates out at 87. Very much on the fringe.
The Cuban Comet wasn't actually a prolific base-stealer after his early 20's, never hit for big power, and despite being consistently above-average and winning three Gold Gloves, won't get much credit for manning left field for most of his career. For a man so associated with longevity, Minoso wasn't a very useful major leaguer after age 35.
If Minoso deserves to be rewarded though, it's for his resilience. Perhaps his multiple comeback attempts after the age of 50 and his career in the Mexican League could be categorized as sideshow, but perhaps it was only an attempt to make up for lost time after Minoso spent three seasons of his physical prime stuck in the Negro Leagues, starting in 1945 before the Major Leagues were desegregated.
Even after being signed by the Indians, Minoso had to wait two more seasons till a trade to the White Sox gave him his first shot as a full-time player at age 25, whereupon he immediately launched into an 11-season prime that saw his wRC+ never dip below 120 until his final year as a regular.
That trade also made Minnie became the first person of color to play for the White Sox, and he absorbed all the hell associated with integrating a professional baseball team in 1950's for his effort.
In fact, if there's a statistic Minoso can hang his hat on, it's his sterling .389 career on-base percentage, which was thanks in no small part to him leading the league in hit-by-pitches 10 different seasons. Which was thanks in no small part to a lot of racism.
Ultimately, if Minoso makes into the Hall of Fame, the Veterans Committee will have to give consideration to his Negro League career and his larger contributions to the sport to push him over the top in spite of major league numbers that are just below the cut.
But if they put Minnie in the Hall partly because they can't pass up on the delicious irony that those who tried to drive him out the game only enhanced his greatness....well, I'd be fine with that too.