What does your religion/belief structure teach about who or what to put before all else? God? Fellow man? Nature/Earth? Self?
To use the term God to describe the Ultimate condition of all being/existence itself, I would say to put God as the first priority is the means to first understand, know, and love yourself in and with that Light, and then as a result of that self transformation into Self, then you are actually capable of loving others, as well as the whole of creation.
In order to help others on a plane in distress, you need to first put on your own oxygen mask which is tapped into the source of the oxygen. Then when you are renewed and made healthy, then you are able to help others - not before. So the order is oxygen first (God/Love), your oxygen mask second (self renewal), others third (the result of one having health to help).
Why do you believe your religion teaches this?
I don't really identify with any religion per se, but my background is Christianity, and the reason it
should teach this, is because it's what Jesus himself taught, "Love God with all your heart, mind, soul and strength, and love your neighbor as yourself. On these two commandments hang all of the law". In other words fulfilling love requires tapping into the Source of Love. Drop the first part and go straight for the second, and its your small self, the egoic needy self, trying to find the source of its strength in others. Finding God within is awakening that inner Light which is not dependent on any external sources which can be depleted. That Love is timeless and inexhaustible.
Bonus question: If you answer anything other than self, where is your own and/or your religion's line between a minor self-sacrifice to put someone's/something's needs before your own and total self-annihilation?
The line is the source of that love. Is it your ego self, or the Self which it eternal? When it is the Self, the ego self is merely a conduit, not the source. If the ego self is the source, you will not be able to truly put others' needs before your own. Often times, those that appear very "giving" are actually only seeking for their own ego self, to find acceptance for themselves in the eyes of others, hoping that others will love them for their goodness.
This is not truly "loving your neighbor as yourself", because you don't first have that love of self, which is pure and unconditional. How can one truly forgive another when they can't forgive themselves? How can one truly love another when they don't know what it is to love themselves first?