Which of these keepers should I keep for my fantasy baseball league?

Most people would say Puig based on his age and potential. There is a health and attitude concern, though. Ellsbury is an injury risk and legs go before power. Ramirez SHOULD be one of the best players in the game, but something always seems to happen to him. Fielder may wake up his home run power in Texas, but why keep him when Freeman has it all and is younger.

And unless you think Braun got all his skills from PEDs, he is the other must keep. Of the other 4, I would keep Ramirez and Puig -- but not as strong on them.

With Freemans age and skills, you can lock up first for many years. Hanley is in a walk year so while he is an injury risk, he plays at a shallow position and is playing for a contract so there is incentive there. Braun would be third for me. Look at his minor league numbers all the way through the majors. Unless he was juicing from day one in the minors (highly doubtful), I don't see any reason for him not to return to putting up his past numbers.

As for number 4, this comes down to what stat you want to go after more. If you want to lock up steals and runs then Ellsbury is your guy. Combined with Hanley & Braun you've got 3 guys to swipe bags for you so if you add someone like Altuve at 2nd you can compete in steals weekly without adding a one trick SB pony.

If you want power it Puig or Fielder. Both are good options and come down to a matter of preference. I like Fielder more as I would rather have a big bat to back up my first baseman incase something happens like an injury. And as FarOutside mentioned, there is the maturity issue with Puig plus there is also the potential for regression in his second year.