If you look at the list of
top 20 players with the most WS rings, 19 of them won all or most of their rings with the Yankees. Only Eddie Collins made the list without the help of being on the Yankees.
No Cobb, Williams, Mays, Aaron, Mathewson, Young, Koufax, Foxx, W Johnson, Clemente, Trout, Bench, Schmidt, Morgan, Seaver, Ryan, etc.
Over half of the top 20 championship ring holders are not even in the HOF. Johnny Murphy who?
Looks to me like you just had to be on the Yankees sometime from the 1930s to the 1950s and collect your rings.
And as far as the OP's question, I'd list, in order:
1. Aaron
2. Mays
3. Foxx
4. Hornsby
Since 'The Greatest' is not a counting stat, it depends on how you weigh certain things like average vs power, peak vs. longevity, runs produced vs on-base percentage, etc. With so many great players, there is no single right answer.