1. You cannot ignore Ty Cobb. The highest batting average of all time, #2 in hits ever, 897 stolen bases, a Triple Crown, 168 career OPS+ (Pete Rose never once had a season even approaching a 168 OPS+), 151+ WAR, one of the top totals of all time. Although he has a reputation as a singles hitter, he lead the league in slugging percentage 8 times. Cobb, as a human being, has a mixed legacy, not as bad as some of the stories, not as racist as some of the stories (some of which were just absolutely made up), but also not a stereotypical "nice guy" ahead of his time. He appears capable of both great individual kindness, as well as a lot of misanthropy. You have to discount Cobb's numbers some because he played before desegregation, and in leagues with a smaller base of players. Then again, he played most of his career in a pitcher's era, with crappy baseballs that the pitchers could scuff, mutilate, spit and spindle. I cannot see how he can be anything but the #1 Tiger.
2. Al Kaline. Mr. Tiger. A genuinely nice guy and great ballplayer. Could hit, run, field, throw and hit for power. Spent a big chunk of his career in the #1 pitcher's era in baseball history and still had great numbers.
3. Justin Verlander. It comes down to Verlander, Newhouser, Lolich or Bridges as the greatest ever Tiger pitcher. Newhouser won back to back MVPs and was utterly dominant over a 5 year stretch (44-48) but that was during WWII with the player pools depleted and mostly before desegregation. Verlander's peak was not quite as good numerically, but was pretty amazing, and plays against global competition (Hispanic, Asian, all Americans). Verlander helped bring the team back from its darkest age. Tommy Bridges, by the way, is almost totally forgotten, but played his entire career with the Tigers, served in WW II while still an effective pitcher, and was the ace on 3 WS teams. Again, he gets the pre-integration discount, but he was an awfully good player.
4. Lou Whitaker/Charlie Gehringer. Sweet Lou was an incredibly player. Why the *%$k isn't he in the Hall of Fame with Tram? 75.1 WAR. He hit with power. He walked more than he struck out in his career. He was a slap hitter when he started in Detroit, and then developed rooftop power. He never had one outstanding season where he would have drawn MVP attention. Instead, he was just consistently great year after year after year. Gehringer was a very similar player to Whitaker, also consistently great. He may have been slightly better, but Lou (obviously) played post-integration. It is hard for me to separate them, so I'll put them together.
5. Hank Greenberg/Miguel Cabrera. Each was the best, or close to the best hitter in baseball of their time. Greenberg had a short career, in part because of 3 years of service in World War II, and played pre-integration. However, he was a vocal supporter of Jackie Robinson and faced his own harassment over his religion. Miggy -- we may forget how great a hitter he was because of his injuries the last 3 years. Between 2009 and 2016, however, he was absolutely amazing, putting astronomical OPS+ numbers up, winning a Triple Crown and, together with Verlander, leading one of the two most successful eras of Tiger baseball (2006-2015 and 1934-1945).
Honorable mentions: Hal Newhouser, Mickey Lolich, Tommy Bridges, Jim Bunning, Harry Heilman, Alan Trammell, Bill Freehan, Sam Crawford.