The greater good sounds to me like something that, in the long term, provides the greatest amount of good to the greatest amount of people. Things like this may include doing things that may include things that may make someone angry, but benefit them in the long term (ie, if you refuse to let your kid eat at McDonalds, he'll be angry at you, but in the long run it'll be better for him because he won't die of 50 heart attacks)
Utilitarians (people who want the greater good) are also willing to do evil things in order to achieve that greater good ("The ends justify the means.") This means that a utilitarian would kill an innocent person in cold blood if doing so would end up saving three innocent people.
Happiness, on the other hand, has its downfalls as well. A sadist may feel happy when he harms people, but that doesn't make it a good thing.
Personal gain, well. A lot of people who are only out for personal gain often screw others over in their pursuit for it (see: people who buy mass quantities of high demand stuff on EBay, such as XBox360's and then sell them for exorbitant amounts of money), as opposed to achieving personal gain through honest, hard work.
I think if there were a community where everyone looked after everyone's best interests, people would be happier than those in a sort of "every man for himself" community.
From what I know (or think I know) about the three choices, I'd go with the greater good.
EDIT: John, the actual event you experienced seems like something other than "for the greater good." It sounds to me like the complete opposite. "Let's have you lazy/dumb asses leech off the hard worker, rather than having to face a challenge and overcome it yourself." I think the greater good in that situation would be for the teacher to essentially say "get your shit together and actually accomplish something through hard work. That way, you'll improve yourselves, and in the end, you'll have gained something through the experience."
Then again, maybe the greater good and personal gain can be compared to Communism/Capitalism respectively.
Overall, this is a good poll, and I feel like I could learn a lot from it. Good work, Easykill.