The best things to learn with every GF are the stat 'bonus' abilities. You get these from learning all the stat +x% abilities (example str +20%, str +40%, etc), and it will then appear (in this case 'str bonus'). With this equipped when you lv up the appropriate stat will increase more, allowing you to have really high base stats so you can junction your stronger spells to better things (like ultima to elemental def, pain to status atk or def, etc). Another way to increase stats ENORMOUSLY is if you spend the time using the 'devour' ability that Eden learns or you can teach to GFs.