OK - I think I have my selections. Both Group B
1989, 1990, 1991, 1992, 1993 Kansas City Royals
1979, 1980, 1981, 1982, 1983 California Angels
So my four selections include...
1894-1898 Baltimore Orioles (Group C)
1963-1967 Chicago White Sox (Group A)
1989-1993 Kansas City Royals (Group B)
1979-1983 California Angels (Group B)
That basically gives me 80+ years of a Group A team (not White Sox) to find a starting 1B or OF. I think I can manage that o.k.