My guess is the second greatest good would be the best option. Taking into account that these are mortal beings and you don't know how long will these people live/be healthy, the best choice would be one that is not the least rewarding (first greatest good) neither the slowest to come.
Think of it as spending your life savings: you don't want to spend it all on your youth and be poor the rest of your life and you don't want to spend it all in your nineties either, when you'll be too old to enjoy it. The answer is somewhere in the middle.
The first greatest good for the greatest number for the greatest number will start "first" (by whatever measurement is applied) but ends before the second greatest good ends and doesn't last as long (in total) as the third greatest good.
The second greatest good for the greatest number will start end "last" (by whatever measurement is applied), but does not last as long as the third greatest good (in total)and doesn't start as soon as the first greatest good.
The third greatest good for the greatest number lasts the longest (in total), but ends before the second greatest good ends and starts after the first greatest good starts.
What within utilitarianism allows for selecting between these three greatest good for the greatest number?