Pay your taxes, don't default on your taxes, try not to get too many traffic tickets. If you get few that's OK, but if you get too many that can be ground for troubles. Don't get into any criminal plot, as you can lose your Green Card if you have a felony conviction. There are other things that can hurt your Green Card like DUI more than one or two of them then you can get into trouble. So, as long as you are like regular people I don't think there is anything to worry about.